Exponents & Radicals

Problem 1701

Solve for $v$ : $v-4=\sqrt{26-5 v}$ . If multiple solutions, separate with commas; if none, state "No solution".

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Problem 1702

Solve for $u$ in the equation $\sqrt{18-u}=u+2$ . What are the real solutions?

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Problem 1703

Solve for $u$ : $(5u+6)^{\frac{1}{4}} + 5 = 2$ . If multiple solutions, separate with commas; if none, state "No solution".

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Problem 1704

Solve for $v$ in the equation $(9 v+10)^{\frac{1}{3}}+4=8$ .

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Problem 1705

Simplify $\sqrt{28 x^{10} y^{11}}$ to the form $a \sqrt{b}$ . $\sqrt{28 x^{10} y^{11}}=$

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Problem 1706

A proton (rest mass $1.67 \times 10^{-27} \mathrm{~kg}$ ) has total energy that is 3.4 times its rest energy. What is a) the kinetic energy of the proton?
b) the magnitude of the momentum of the proton? $\square$ $\times 10^{-18} \mathrm{~kg} \cdot \mathrm{~m} / \mathrm{s}$ . c) the speed of the proton? $\square$ c.

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Problem 1707

Question 4 of 10 Which choice is equivalent to the product below? $\sqrt{8} \cdot \sqrt{5}$ A. $10 \sqrt{2}$ B. $\sqrt{13}$ C. $2 \sqrt{10}$ D. $4 \sqrt{10}$

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Problem 1708

Question 10 of 10 Which choices are equivalent to the quotient below? Check all that apply. $\frac{\sqrt{12}}{\sqrt{6}}$ A. $\frac{\sqrt{6}}{2}$ B. $\frac{2}{\sqrt{3}}$ C. $\frac{\sqrt{4}}{\sqrt{2}}$ D. 2 E. $\frac{\sqrt{5}}{\sqrt{2}}$ F. $\sqrt{2}$

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Problem 1709

Question 2 of 10 Write $\sqrt{a^{8} a^{3}}$ as an algebraic expression using a rational exponent. A. $a^{12}$ B. $a^{11 / 3}$ c. $a^{2 / 24}$ D. $a^{11 / 2}$

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Problem 1710

Question 9 of 10 What is the value of the expression below? $\left(81^{2}\right)^{18}$ A. 27 B. 3 C. 9 D. 1

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Problem 1711

Identify the base and the exponent in each expression. See Example 1. Look Alikes . . .
13. a. $4^{3}$ b. $-4^{3}$ c. $(-4)^{3}$

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Problem 1712

Simplify the expression: $\frac{20 \sqrt{3}}{5 \sqrt{3}}$ .

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Problem 1713

Cuotient of expressions involving expon
Simplify. $\frac{z^{3} x^{6}}{z^{5} x^{6}}$

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Problem 1714

Simplify. $\frac{x^{5} y^{4}}{x^{3} y^{6}}$

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Problem 1715

www-awu.aleks.com/alekscgi/x/lsl.exe/1o_u
Exponants and Pefyromials Introduction to the power rules of exponente
Simplifi. $\left(x^{2}\right)^{3}$
Write your answer without parentheses.

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Problem 1716

Radieal Cube root of an integer
Find the value of $\sqrt[3]{1000}$ $\square$

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Problem 1717

Rewrite the following without an exponent. $\left(\frac{8}{9}\right)^{-1}$

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Problem 1718

Simplify $5 b^{4} \times 5 b$

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Problem 1719

線分 $A B$ 上に 2 点 $\mathrm{P}, \mathrm{Q}$ がある。 $A P: P B=\frac{\sqrt{14}}{3}: \sqrt{\frac{7}{2}}$ , $\mathrm{AQ}: \mathrm{QB}=\sqrt{\frac{5}{3}}: \sqrt{\frac{3}{5}}$ であるとき, $\mathrm{AP}: \mathrm{PQ}$ を最も簡単な整数比で表せ。

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Problem 1720

fare lo stesso per $(\sqrt{2}-\sqrt{3})^{-1}$ .

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Problem 1721

r with a positive exponent. c) $\left(-9^{4}\right)^{-1}$ f) $\left[\left(7^{-3}\right)^{-2}\right]^{-2}$

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Problem 1722

1. Rewrite each expression as an equivalent expression with a positive exponen a) $5^{-4}$ c) $\frac{1}{2^{-4}}$ e) $\left(\frac{3}{11}\right)^{-1}$ b) $\left(-\frac{1}{10}\right)^{-3}$ d) $-\left(\frac{6}{5}\right)^{-3}$ f) $\frac{7^{-2}}{8^{-1}}$
2. Write each expression as a single power with a positive exponent. a) $(-10)^{8}(-10)^{-8}$ c) $\frac{2^{8}}{2^{-5}}$ e) $\left(-9^{4}\right)^{-1}$ b) $6^{-7} \times 6^{5}$ d) $\frac{11^{-3}}{11^{5}}$ f) $\left[\left(7^{-3}\right)^{-2}\right]^{-2}$
3. Which is the greater power, $2^{-5}$ or $\left(\frac{1}{2}\right)^{-5}$ ? Explain.

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Problem 1723

Add. Write your answer in simplest form. $-2 \sqrt{5}+9 \sqrt{5}$ $\square$ $\square$ Submit

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Problem 1724

Write $4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$ in exponential notation. $4^{7}$ $4^{G}$ $7^{4}$ 16,384

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Problem 1725

(1 point) Simplify the given expression and enter your answer with positive exponents. $y^{-3}\left(2 y^{4}\right)^{7}$
Simplified answer: $\square$ help (formulas)

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Problem 1726

(1 point) Simplify the given expression and enter your answer with positive exponents. $\frac{6 j k^{7}}{j^{-7}}$
Simplified answer: $\square$ help (formulas)

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Problem 1727

(2 points) Solve the rational exponent equation. Use factoring where necessary, If there is more than one answer, enter a comma separated list. $x^{2 / 3}=4$ $x=$ $\square$ holp (numbers)

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Problem 1728

Simplify. $\frac{y^{7}}{y^{-3}}$
Write your answer with a positive exponen

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Problem 1729

Simplify. $\frac{x^{-2}}{x^{-8}}$
Write your answer with a positive exponent

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Problem 1730

Simplify. -8 X 9 X Write your answer with a positive exponent only. ☐ X

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Problem 1731

Simplify. $\frac{x^{-8}}{x^{9}}$
Write your answer with a positive exponent only.

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Problem 1732

Find the value of $\frac{\left(x^{2}\right)^{3}}{x^{2}}$ when $x=3$ . Choices: 81, 27, 9, 6.

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Problem 1733

Find expressions equivalent to $\sqrt{80}$ , $80^{\frac{1}{2}}$ , $4 \sqrt{5}$ , $4 \sqrt{10}$ , $8 \sqrt{5}$ , $160^{\frac{1}{2}}$ .

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Problem 1734

Calculate the product of $5 \times 10^{22}$ and $1 \times 0.5^{10}$ .

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Problem 1735

Find the wavelength(s) of light that can't remove an electron from cesium given the energy is $376 \mathrm{~kJ/mol}$ . Choices: $200 \mathrm{~nm}$ , $242 \mathrm{~nm}$ , $320 \mathrm{~nm}$ .

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Problem 1736

Lesson 5 - Negative Rational Exponents
1. Write $7^{-\frac{2}{3}}$ without exponents.
2. Write $\sqrt[4]{11^{5}}$ without radicals.

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Problem 1737

6. A student forgets to turn off a $6.00 \times 10^{2} \mathrm{~W}$ block heater of a car when the weather turns warm. If 14 h goes by before he shuts it off, how much energy is used by the heater? (Hint....think back to unit 3 energy formulas). (you answer)

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Problem 1738

Multiply. $6 w^{8} u^{6} \cdot 2 u^{8} \cdot 4 w$
Simplify your answer as much as possible.

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Problem 1739

Rewrite without parentheses and simplify. $(3+u)^{2}$

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Problem 1740

Rewrite without parentheses and simplify. $(6 w+7)^{2}$

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Problem 1741

(a) The $\left[\mathrm{H}^{+}\right]$ of a solution is $2.7 \times 10^{-6}$ Calculate the pH . (b) The $\left[\mathrm{OH}^{-}\right]$ of a solution is $3.2 \times 10^{-8}$ Calculate the pOH . (c) The $\left[\mathrm{H}^{+}\right]$ of a solution is $5.4 \times 10^{-3}$ Calculate the $\left[\mathrm{OH}^{-}\right]$ . (d) The $\left[\mathrm{OH}^{-}\right]$ of a solution is $1.8 \times 10^{-9}$ Calculate the $\left[\mathrm{H}^{+}\right]$ .

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Problem 1742

Add. Write your answer in simplest form. $8 \sqrt{10}+8 \sqrt{40}$ $\square$ Submit

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Problem 1743

20 Rationalise the denominator and simplify $1 \frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}-\sqrt{18}}$

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Problem 1744

(a) $3^{-2} \times 3^{x}=81$
Find the value of $x$ . $3^{-2} \times 3^{x}=3^{4} \quad 3^{-2} \times 3^{x}$ $(x)=4$ $\frac{4}{2} 2$ (b) $x^{-\frac{1}{3}}=32 x^{-2}$ $\begin{array}{c} 3^{-2}+3^{4}-3 \\ =3 \end{array}$
Find the value of $x$ .

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Problem 1745

$(-2 a)^{4}$

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Problem 1746

$\frac{5 \sqrt{6}}{-\sqrt{3}}$

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Problem 1747

Simplify: $-6(\sqrt{36 t}+3-\sqrt{t})$ $-48 \sqrt{t}$ $-30 \sqrt{t}+18$ None of these. $48 \sqrt{t}$ $-30 \sqrt{t}-18$

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Problem 1748

expression
1. $8 \times 8 \times 8 \times 8 \times 8 \times 8 \times$ 2.4 $4=4$
3. $-10 \times(-10) \times(-10) \times$
Evaluate each expressio $4.9^{2}=81$
6. $3,105^{\circ}$
8. $(-2)^{7}$

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Problem 1749

Solve $u^{2}=16$ , where $u$ is a real numbe Simplify your answer as much as pc
If there is more than one solution, If there is no solution, click on "No $u=$ $\square$

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Problem 1750

Simplify 20 - 6 + 8 ÷ 2^{3}. What is the result?

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Problem 1751

Solve for $x$ : $x^{\frac{1}{3}}=2$ .

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Problem 1752

Rewrite $x^{-3}$ as a fraction.

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Problem 1753

What is the value of $(\sqrt[3]{x})^{0}$ ?

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Problem 1754

Simplify $(\sqrt[3]{x})^{6}$ .

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Problem 1755

Simplify the expression $\left(\frac{y^{5}}{8 x^{6} y^{8}}\right)^{-\frac{1}{3}}$ .

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Problem 1756

Simplify $(\sqrt[3]{x})^{6}$ .

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Problem 1757

Find the equivalent expression for $x^{6} x^{2}$ . Options: $x^{4} x^{3}$ , $x^{5} x^{3}$ , $x^{7} x^{3}$ , $x^{9} x^{3}$ .

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Problem 1758

How many years does light take to travel $3.65 \times 10^{8}$ miles if a light year is $5.87 \times 10^{12}$ miles?

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Problem 1759

? Question Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the expressions with their simplified forms.
Tiles $\frac{1}{2}$ $5 \sqrt{3}$ $2 \sqrt{5}$ $4 \sqrt{5}$ 4
Pairs $\sqrt{2} \cdot \sqrt{8}$ $\qquad$ $\sqrt{80}$ $\frac{\sqrt{5}}{\sqrt{20}}$ $\qquad$ $\square$ $\square$ $\sqrt{20}$ $\qquad$

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Problem 1760

Tiles $5 \sqrt{3}$ $2 \sqrt{5}$
Pairs $\begin{array}{cc} \sqrt{2} \cdot \sqrt{8} & \longrightarrow \\ \sqrt{80} & \longrightarrow \\ \frac{\sqrt{5}}{\sqrt{20}} & \longrightarrow \\ \sqrt{20} \end{array}$

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Problem 1761

Part A $3 \pi+\frac{2 \pi}{3}$
Space used (includes formatting): $0 / 30000$ Submit
Part B $3 \sqrt{5}+15 \sqrt{5}$

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Problem 1762

Expressions with Irrational Numbers: Tutorial ? Question Drag each expression to the correct location. Estimate the value of each irrational expression to the nearest integer. $\begin{array}{lllll} -3 \sqrt{4} \cdot \sqrt{3}+2 \sqrt{9} \cdot \sqrt{3} & \frac{-\sqrt{20}}{-\sqrt{21}} & \frac{2 \sqrt{2}+3 \sqrt{2}}{5 \sqrt{2}} & -\frac{3 \pi}{3 \sqrt{10}} & 4 \cdot 3 \sqrt{2}-2 \sqrt{2} \cdot \sqrt{36} \end{array}$ $-\frac{3 \pi}{3 \sqrt{10}}$

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Problem 1763

Evaluate. Write your answers as fractions. $\begin{array}{r} \frac{-2}{5^{2}}= \\ \left(-\frac{1}{3}\right)^{3}= \end{array}$

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Problem 1764

An OB/GYN physician in private practice knows her malpractice insurance will be $\$ 75,000$ and is due in one year. How much should she deposit into an account each month if that account has an annual rate of $4.0 \%$ compounded monthly and she wishes to pay it in full knowing that the insurance company drops the price by $2 \%$ if paid in full? Round your answer to two decimal places. Do not include the $\$$ sign in your answer. Hint: Lower the price by $2 \%$ as she is planning on paying in full. Your Answer:

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Problem 1765

Change each of the following to a radical, and then evaluate each power without using a calculator. Justify your answer. B). $\left(\frac{9}{16}\right)^{\frac{3}{2}}$

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Problem 1766

Evaluate the expression for $r=8, s=2$ , and $t=-0.8$ . Write your answer as a decimal or whole number. $r s^{2} t-r=$ $\square$ Submit

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Problem 1767

(a) Simplify $\left(2 c^{4} d^{7}\right)^{3}$

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Problem 1768

(4. $3 \sqrt[3]{108}$

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Problem 1769

$\left(\frac{2}{\sqrt{3}-2}\right) \cdot\left(\frac{2 \sqrt{3}-1}{2}\right)$

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Problem 1770

Find the distance $d(A, B)$ between points $A$ and $B$ . $\begin{array}{l} A(10,2) ; B(-1,-8) \\ (A, B)=\square \end{array}$ $\square$ Simplify your answer. Type an exact answer, using radicals as needed.)

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Problem 1771

10. Create 3 expressions that are equivalent to: $\frac{\sqrt{a^{5}}}{\sqrt[3]{a^{4}}}$

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Problem 1772

Question 7 (1 point) Write the following expression in radical form: $16^{0.25}$ $\sqrt[2]{16^{2}}$ $\sqrt{4}$ $\sqrt{16}$ $\sqrt[4]{16}$

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Problem 1773

Find the number of parts, $n$ , produced when the cost, $C$ , is \ $4,200 in the equation$ C=200 \sqrt[3]{n}+200$.

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Problem 1774

Simplify: $\frac{\sqrt{6 x^{3}}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$ and find the result among these: $16 x^{4}$ , $\sqrt{16 x^{4}}$ , $4 x \sqrt{x^{3}}$ , $4 x^{2}$ .

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Problem 1775

Find the equivalent expression for $\left(\frac{1}{z^{3 / 5}}\right)^{-1 / 5}$ . A. $z^{3 / 25}$ B. $z^{-3 / 25}$ C. $z^{-2 / 5}$ D. $z^{2 / 5}$

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Problem 1776

Which expression is equivalent to $\sqrt[3]{64 y}$ ? $128 y^{\frac{1}{3}}$ $8 y$ $8 y^{\frac{1}{3}}$ $4 y^{\frac{1}{3}}$ Submit

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Problem 1777

Solve for $x$ . $143+(12 x+76)^{\frac{7}{6}}=15$
Write one solution in each box. You can add or remove boxes. If there are no solutions, remove all boxes. $\square$ Submit

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Problem 1778

positive solution of the equation. $8 x^{\frac{4}{5}}+4=32772$

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Problem 1779

What is $\sqrt{9 x^{0}+8 y^{0}+3}$ in its SIMPlest torm?

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Problem 1780

Simplify, using only positive exponents in your answer. $\frac{x^{-5}+y^{-4}}{x^{-4}+y^{-3}}$

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Problem 1781

5-77. A bond has a face value of $\$ 1,000$ , is redeemable in eight years, and pays interest of $\$ 100$ at the end of each of the eight years. If the bond can be purchased for $\$ 981$ , what is the rate of return if the bond is held until maturity? (5.3) (a) $10.65 \%$ (b) $12.65 \%$ (c) $10.35 \%$ (d) $11.65 \%$

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Problem 1782

1) Développe $(\sqrt{5}+1)^{2}$ et $(\sqrt{5}-1)^{2}$ . En déduire une expression plus simple de $A=\sqrt{6+2 \sqrt{5}} \quad \text { et } B=\sqrt{6-2 \sqrt{5}}$

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Problem 1783

Simplify the expression $\left(\frac{3 a^{5} b^{5}}{a b^{2}}\right)^{2}$ A $9 a^{8} b^{6}$
B $6 a^{8} b^{6}$
C $6 a^{16} b^{9}$
D $9 a^{6} b^{5}$

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Problem 1784

$\frac{\left(2 x^{6}\right)^{3}}{\left(8 x^{5}\right)^{2}}$
Write your answer using only positive exponents.

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Problem 1785

Order the expressions by choosing $>,<$ , or $=$ . $\begin{array}{ll} 2^{4} \times 2^{2} & \square \end{array} 2^{8}$
$x$

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Problem 1786

$\begin{array}{l}\sqrt{144} \cdot 12=144 \\ 12^{12}-12^{12}=0\end{array}$

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Problem 1787

Solve for $x$ . Find all solutions. $(x-10)^{\frac{4}{5}}=256$
Raise both sides to the power of $\frac{5}{4}$ to eliminate the fractional exponent.

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Problem 1788

1. Write each expression as a single power. Then, evaluate. (4)
Single Power Evaluate a) $2^{4} \times 2^{4}$ $\qquad$ $\qquad$ b) $(-4)^{2} \times(-4)^{2}$ $\qquad$ $\qquad$ c) $6^{2} \times 6$ $\qquad$ $\qquad$ d) $9^{3} \times 9^{3}$ $\qquad$ $\qquad$

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Problem 1789

Simplify. $\sqrt{12 y^{13}}$
Assume that the variable represents a positive real number.

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Problem 1790

Simplify the expression. Assume that all variables represent nonzero numbers. $\begin{array}{l} 3\left(-x y^{2}\right)\left(x^{7} y\right) \\ 3\left(-x y^{2}\right)\left(x^{7} y\right)= \end{array}$ $\square$ (Use positive exponents only.)

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Problem 1791

$[8(10+30)-1] \times 10^{2}$

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Problem 1792

Calculate. $\frac{5 \times 10^{7}}{4 \times 10^{4}}$
Write your answer in scientific notation.

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Problem 1793

Write an expression for the sequence of operations described below. raise 7 to the 4th power, then divide the result by $y$ Do not simplify any part of the expression. $\square$

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Problem 1794

You borrowed $\$ 59,000$ for 2 years at $11 \%$ which was compounded annually. What is the total? ,693.90 \$1,363.90 \$72,693.90 \$73,793.90

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Problem 1795

Find $p$ in $x^{3} \cdot x^{2}=x^{p}$ and $r$ in $\left(x^{3}\right)^{2}=x^{r}$ .

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Problem 1796

Step 1: $\quad$ Subtract the exponents of powers with like bases. $\left(\frac{x^{6} y}{2}\right)^{-2}$
Step 2: Apply the power of a product rule. $\frac{x^{-12} y^{-2}}{2^{-2}}$
Step 3: Write negative exponents as reciprocals using positive exponents. $\frac{1}{2^{2} x^{12} y^{2}}$
Step 4: Evaluate the power with the integer base. $\frac{1}{4 x^{12} y^{2}}$
In which step did Loi make the first error?

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Problem 1797

$\frac{\sqrt{3 x} \cdot 3 x}{2}-\frac{2 x \cdot x^{2 / 3 \sqrt{3} x}}{2}$

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Problem 1798

QUESTION 2 Multiply and simplify completely. $(2-\sqrt{6})(4+\sqrt{6})$ $\square$

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Problem 1799

Simpliby mo expression $x^{4} y^{3} \cdot x^{2} y^{8}$

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Problem 1800

Radicals
Use the product rule to simplify the radical. $\begin{array}{c} \sqrt{54} \\ \sqrt{54}=\square \end{array}$ $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.)

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1 ...15 16 17 18 19

Exponents & Radicals

Problem 1701

Solve for vvv: v−4=26−5vv-4=\sqrt{26-5 v}v−4=26−5v​. If multiple solutions, separate with commas; if none, state "No solution".

Problem 1702

Solve for uuu in the equation 18−u=u+2\sqrt{18-u}=u+218−u​=u+2. What are the real solutions?

Problem 1703

Solve for uuu: (5u+6)14+5=2(5u+6)^{\frac{1}{4}} + 5 = 2(5u+6)41​+5=2. If multiple solutions, separate with commas; if none, state "No solution".

Problem 1704

Solve for vvv in the equation (9v+10)13+4=8(9 v+10)^{\frac{1}{3}}+4=8(9v+10)31​+4=8.

Problem 1705

Simplify 28x10y11\sqrt{28 x^{10} y^{11}}28x10y11​ to the form aba \sqrt{b}ab​. 28x10y11=\sqrt{28 x^{10} y^{11}}=28x10y11​=

Problem 1706

Problem 1707

Question 4 of 10 Which choice is equivalent to the product below? 8⋅5\sqrt{8} \cdot \sqrt{5}8​⋅5​ A. 10210 \sqrt{2}102​ B. 13\sqrt{13}13​ C. 2102 \sqrt{10}210​ D. 4104 \sqrt{10}410​

Problem 1708

Problem 1709

Question 2 of 10 Write a8a3\sqrt{a^{8} a^{3}}a8a3​ as an algebraic expression using a rational exponent. A. a12a^{12}a12 B. a11/3a^{11 / 3}a11/3 c. a2/24a^{2 / 24}a2/24 D. a11/2a^{11 / 2}a11/2

Problem 1710

Question 9 of 10 What is the value of the expression below? (812)18\left(81^{2}\right)^{18}(812)18 A. 27 B. 3 C. 9 D. 1

Problem 1711

Identify the base and the exponent in each expression. See Example 1. Look Alikes . . .13. a. 434^{3}43 b. −43-4^{3}−43 c. (−4)3(-4)^{3}(−4)3

Problem 1712

Simplify the expression: 20353\frac{20 \sqrt{3}}{5 \sqrt{3}}53​203​​.

Problem 1713

Cuotient of expressions involving exponSimplify. z3x6z5x6\frac{z^{3} x^{6}}{z^{5} x^{6}}z5x6z3x6​

Problem 1714

Simplify. x5y4x3y6\frac{x^{5} y^{4}}{x^{3} y^{6}}x3y6x5y4​

Problem 1715

www-awu.aleks.com/alekscgi/x/lsl.exe/1o_uExponants and Pefyromials Introduction to the power rules of exponenteSimplifi. (x2)3\left(x^{2}\right)^{3}(x2)3Write your answer without parentheses.

Problem 1716

Radieal Cube root of an integerFind the value of 10003\sqrt[3]{1000}31000​ □\square□

Problem 1717

Rewrite the following without an exponent. (89)−1\left(\frac{8}{9}\right)^{-1}(98​)−1

Problem 1718

Simplify 5b4×5b5 b^{4} \times 5 b5b4×5b

Problem 1719

Problem 1720

fare lo stesso per (2−3)−1(\sqrt{2}-\sqrt{3})^{-1}(2​−3​)−1.

Problem 1721

r with a positive exponent. c) (−94)−1\left(-9^{4}\right)^{-1}(−94)−1 f) [(7−3)−2]−2\left[\left(7^{-3}\right)^{-2}\right]^{-2}[(7−3)−2]−2

Problem 1722

Problem 1723

Add. Write your answer in simplest form. −25+95-2 \sqrt{5}+9 \sqrt{5}−25​+95​ □\square□ □\square□ Submit

Problem 1724

Write 4⋅4⋅4⋅4⋅4⋅4⋅44 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 44⋅4⋅4⋅4⋅4⋅4⋅4 in exponential notation. 474^{7}47 4G4^{G}4G 747^{4}74 16,384

Problem 1725

(1 point) Simplify the given expression and enter your answer with positive exponents. y−3(2y4)7y^{-3}\left(2 y^{4}\right)^{7}y−3(2y4)7Simplified answer: □\square□ help (formulas)

Problem 1726

(1 point) Simplify the given expression and enter your answer with positive exponents. 6jk7j−7\frac{6 j k^{7}}{j^{-7}}j−76jk7​Simplified answer: □\square□ help (formulas)

Problem 1727

(2 points) Solve the rational exponent equation. Use factoring where necessary, If there is more than one answer, enter a comma separated list. x2/3=4x^{2 / 3}=4x2/3=4 x=x=x= □\square□ holp (numbers)

Problem 1728

Simplify. y7y−3\frac{y^{7}}{y^{-3}}y−3y7​Write your answer with a positive exponen

Problem 1729

Simplify. x−2x−8\frac{x^{-2}}{x^{-8}}x−8x−2​Write your answer with a positive exponent

Problem 1730

Simplify. -8 X 9 X Write your answer with a positive exponent only. ☐ X

Problem 1731

Simplify. x−8x9\frac{x^{-8}}{x^{9}}x9x−8​Write your answer with a positive exponent only.

Problem 1732

Find the value of (x2)3x2\frac{\left(x^{2}\right)^{3}}{x^{2}}x2(x2)3​ when x=3x=3x=3. Choices: 81, 27, 9, 6.

Problem 1733

Find expressions equivalent to 80\sqrt{80}80​, 801280^{\frac{1}{2}}8021​, 454 \sqrt{5}45​, 4104 \sqrt{10}410​, 858 \sqrt{5}85​, 16012160^{\frac{1}{2}}16021​.

Problem 1734

Calculate the product of 5×10225 \times 10^{22}5×1022 and 1×0.5101 \times 0.5^{10}1×0.510.

Problem 1735

Find the wavelength(s) of light that can't remove an electron from cesium given the energy is 376 kJ/mol376 \mathrm{~kJ/mol}376 kJ/mol. Choices: 200 nm200 \mathrm{~nm}200 nm, 242 nm242 \mathrm{~nm}242 nm, 320 nm320 \mathrm{~nm}320 nm.

Problem 1736

Lesson 5 - Negative Rational Exponents1. Write 7−237^{-\frac{2}{3}}7−32​ without exponents.2. Write 1154\sqrt[4]{11^{5}}4115​ without radicals.

Problem 1737

6. A student forgets to turn off a 6.00×102 W6.00 \times 10^{2} \mathrm{~W}6.00×102 W block heater of a car when the weather turns warm. If 14 h goes by before he shuts it off, how much energy is used by the heater? (Hint....think back to unit 3 energy formulas). (you answer)

Problem 1738

Multiply. 6w8u6⋅2u8⋅4w6 w^{8} u^{6} \cdot 2 u^{8} \cdot 4 w6w8u6⋅2u8⋅4wSimplify your answer as much as possible.

Problem 1739

Rewrite without parentheses and simplify. (3+u)2(3+u)^{2}(3+u)2

Problem 1740

Rewrite without parentheses and simplify. (6w+7)2(6 w+7)^{2}(6w+7)2

Problem 1741

Problem 1742

Add. Write your answer in simplest form. 810+8408 \sqrt{10}+8 \sqrt{40}810​+840​ □\square□ Submit

Solve for $v$ : $v-4=\sqrt{26-5 v}$ . If multiple solutions, separate with commas; if none, state "No solution".

Solve for $u$ in the equation $\sqrt{18-u}=u+2$ . What are the real solutions?

Solve for $u$ : $(5u+6)^{\frac{1}{4}} + 5 = 2$ . If multiple solutions, separate with commas; if none, state "No solution".

Solve for $v$ in the equation $(9 v+10)^{\frac{1}{3}}+4=8$ .

Simplify $\sqrt{28 x^{10} y^{11}}$ to the form $a \sqrt{b}$ . $\sqrt{28 x^{10} y^{11}}=$

Question 4 of 10 Which choice is equivalent to the product below? $\sqrt{8} \cdot \sqrt{5}$ A. $10 \sqrt{2}$ B. $\sqrt{13}$ C. $2 \sqrt{10}$ D. $4 \sqrt{10}$

Question 2 of 10 Write $\sqrt{a^{8} a^{3}}$ as an algebraic expression using a rational exponent. A. $a^{12}$ B. $a^{11 / 3}$ c. $a^{2 / 24}$ D. $a^{11 / 2}$

Question 9 of 10 What is the value of the expression below? $\left(81^{2}\right)^{18}$ A. 27 B. 3 C. 9 D. 1

Identify the base and the exponent in each expression. See Example 1. Look Alikes . . .
13. a. $4^{3}$ b. $-4^{3}$ c. $(-4)^{3}$

Simplify the expression: $\frac{20 \sqrt{3}}{5 \sqrt{3}}$ .

Cuotient of expressions involving expon
Simplify. $\frac{z^{3} x^{6}}{z^{5} x^{6}}$

Simplify. $\frac{x^{5} y^{4}}{x^{3} y^{6}}$

www-awu.aleks.com/alekscgi/x/lsl.exe/1o_u
Exponants and Pefyromials Introduction to the power rules of exponente
Simplifi. $\left(x^{2}\right)^{3}$
Write your answer without parentheses.

Radieal Cube root of an integer
Find the value of $\sqrt[3]{1000}$ $\square$

Rewrite the following without an exponent. $\left(\frac{8}{9}\right)^{-1}$

Simplify $5 b^{4} \times 5 b$

fare lo stesso per $(\sqrt{2}-\sqrt{3})^{-1}$ .

r with a positive exponent. c) $\left(-9^{4}\right)^{-1}$ f) $\left[\left(7^{-3}\right)^{-2}\right]^{-2}$

Add. Write your answer in simplest form. $-2 \sqrt{5}+9 \sqrt{5}$ $\square$ $\square$ Submit

Write $4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$ in exponential notation. $4^{7}$ $4^{G}$ $7^{4}$ 16,384

(1 point) Simplify the given expression and enter your answer with positive exponents. $y^{-3}\left(2 y^{4}\right)^{7}$
Simplified answer: $\square$ help (formulas)

(1 point) Simplify the given expression and enter your answer with positive exponents. $\frac{6 j k^{7}}{j^{-7}}$
Simplified answer: $\square$ help (formulas)

(2 points) Solve the rational exponent equation. Use factoring where necessary, If there is more than one answer, enter a comma separated list. $x^{2 / 3}=4$ $x=$ $\square$ holp (numbers)

Simplify. $\frac{y^{7}}{y^{-3}}$
Write your answer with a positive exponen

Simplify. $\frac{x^{-2}}{x^{-8}}$
Write your answer with a positive exponent

Simplify. $\frac{x^{-8}}{x^{9}}$
Write your answer with a positive exponent only.

Find the value of $\frac{\left(x^{2}\right)^{3}}{x^{2}}$ when $x=3$ . Choices: 81, 27, 9, 6.

Find expressions equivalent to $\sqrt{80}$ , $80^{\frac{1}{2}}$ , $4 \sqrt{5}$ , $4 \sqrt{10}$ , $8 \sqrt{5}$ , $160^{\frac{1}{2}}$ .

Calculate the product of $5 \times 10^{22}$ and $1 \times 0.5^{10}$ .

Find the wavelength(s) of light that can't remove an electron from cesium given the energy is $376 \mathrm{~kJ/mol}$ . Choices: $200 \mathrm{~nm}$ , $242 \mathrm{~nm}$ , $320 \mathrm{~nm}$ .

Lesson 5 - Negative Rational Exponents
1. Write $7^{-\frac{2}{3}}$ without exponents.
2. Write $\sqrt[4]{11^{5}}$ without radicals.

6. A student forgets to turn off a $6.00 \times 10^{2} \mathrm{~W}$ block heater of a car when the weather turns warm. If 14 h goes by before he shuts it off, how much energy is used by the heater? (Hint....think back to unit 3 energy formulas). (you answer)

Multiply. $6 w^{8} u^{6} \cdot 2 u^{8} \cdot 4 w$
Simplify your answer as much as possible.

Rewrite without parentheses and simplify. $(3+u)^{2}$

Rewrite without parentheses and simplify. $(6 w+7)^{2}$

Add. Write your answer in simplest form. $8 \sqrt{10}+8 \sqrt{40}$ $\square$ Submit

20 Rationalise the denominator and simplify $1 \frac{\sqrt{48}+\sqrt{32}}{\sqrt{27}-\sqrt{18}}$

$(-2 a)^{4}$

$\frac{5 \sqrt{6}}{-\sqrt{3}}$

Simplify: $-6(\sqrt{36 t}+3-\sqrt{t})$ $-48 \sqrt{t}$ $-30 \sqrt{t}+18$ None of these. $48 \sqrt{t}$ $-30 \sqrt{t}-18$

Solve $u^{2}=16$ , where $u$ is a real numbe Simplify your answer as much as pc
If there is more than one solution, If there is no solution, click on "No $u=$ $\square$

Solve for $x$ : $x^{\frac{1}{3}}=2$ .

Rewrite $x^{-3}$ as a fraction.

What is the value of $(\sqrt[3]{x})^{0}$ ?

Simplify $(\sqrt[3]{x})^{6}$ .

Simplify the expression $\left(\frac{y^{5}}{8 x^{6} y^{8}}\right)^{-\frac{1}{3}}$ .

Simplify $(\sqrt[3]{x})^{6}$ .

Find the equivalent expression for $x^{6} x^{2}$ . Options: $x^{4} x^{3}$ , $x^{5} x^{3}$ , $x^{7} x^{3}$ , $x^{9} x^{3}$ .

How many years does light take to travel $3.65 \times 10^{8}$ miles if a light year is $5.87 \times 10^{12}$ miles?

Tiles $5 \sqrt{3}$ $2 \sqrt{5}$
Pairs $\begin{array}{cc} \sqrt{2} \cdot \sqrt{8} & \longrightarrow \\ \sqrt{80} & \longrightarrow \\ \frac{\sqrt{5}}{\sqrt{20}} & \longrightarrow \\ \sqrt{20} \end{array}$

Part A $3 \pi+\frac{2 \pi}{3}$
Space used (includes formatting): $0 / 30000$ Submit
Part B $3 \sqrt{5}+15 \sqrt{5}$

Evaluate. Write your answers as fractions. $\begin{array}{r} \frac{-2}{5^{2}}= \\ \left(-\frac{1}{3}\right)^{3}= \end{array}$

Change each of the following to a radical, and then evaluate each power without using a calculator. Justify your answer. B). $\left(\frac{9}{16}\right)^{\frac{3}{2}}$

Evaluate the expression for $r=8, s=2$ , and $t=-0.8$ . Write your answer as a decimal or whole number. $r s^{2} t-r=$ $\square$ Submit

(a) Simplify $\left(2 c^{4} d^{7}\right)^{3}$

(4. $3 \sqrt[3]{108}$

$\left(\frac{2}{\sqrt{3}-2}\right) \cdot\left(\frac{2 \sqrt{3}-1}{2}\right)$

Find the distance $d(A, B)$ between points $A$ and $B$ . $\begin{array}{l} A(10,2) ; B(-1,-8) \\ (A, B)=\square \end{array}$ $\square$ Simplify your answer. Type an exact answer, using radicals as needed.)

10. Create 3 expressions that are equivalent to: $\frac{\sqrt{a^{5}}}{\sqrt[3]{a^{4}}}$

Question 7 (1 point) Write the following expression in radical form: $16^{0.25}$ $\sqrt[2]{16^{2}}$ $\sqrt{4}$ $\sqrt{16}$ $\sqrt[4]{16}$

Find the number of parts, $n$ , produced when the cost, $C$ , is \ $4,200 in the equation$ C=200 \sqrt[3]{n}+200$.

Simplify: $\frac{\sqrt{6 x^{3}}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$ and find the result among these: $16 x^{4}$ , $\sqrt{16 x^{4}}$ , $4 x \sqrt{x^{3}}$ , $4 x^{2}$ .