Simplify

Problem 1301

11 Simplify the expression. (2 Points) $\left(4 n^{4}-8 n+4\right)-\left(8 n^{2}+4 n^{4}+1\right)$ $-8 n^{2}-8 n+3$ $8 n^{4}+16 n+3$ $-16 n^{2}+3$

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Problem 1302

d $\frac{x^{2} y^{3} \times x^{2} y^{4}}{x^{3} y^{5}}$ f $\frac{r^{4} s^{7} \times r^{4} s^{7}}{A_{c}^{7}}$

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Problem 1303

Find the partial fraction decomposition. $\frac{-16}{x^{3}+4 x}$

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Problem 1304

$-\frac{24}{\sqrt{72}}, \quad \frac{-21}{\sqrt{63}}, \quad \frac{42}{\sqrt{126}}, \quad \frac{52}{4 \sqrt{52}}, \quad \frac{48}{4 \sqrt{96}}, \quad \frac{18}{\sqrt{72}}, \quad \frac{50}{\sqrt{150}}, \quad \frac{-80}{\sqrt{240}}$
Rationalize the denominators of the fractions listed above.

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Problem 1305

Simplify $(3+\sqrt{2})(3-\sqrt{2})$ . a. $3^{\frac{1}{2}}$ c. 7 b. $\frac{1}{2}$ d. 6
Please select the best answer from the choices provided A B C D Mark this and retum

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Problem 1306

Simplify $\sqrt{0.08^{12}}$ a. $(0.08)^{6}$ c. $(0.16)^{6}$ b. $(0.8)^{6}$ d. $(0.12)^{8}$
Please select the best answer from the choices provided A B C D

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Problem 1307

Evaluate. $\frac{5}{7}\left(\frac{2}{3}\right)^{2}+\frac{1}{9}$
Write your answer in simplest form.

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Problem 1308

Evaluate. $-\frac{1}{9}-\left(-\frac{4}{15}\right)$
Write your answer in simplest form.

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Problem 1309

Rewrite the following without an exponent. $4^{-4}$

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Problem 1310

$76[8+6(b-1)]$

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Problem 1311

1) 敨, Simplify. Assume $t$ is greater than or equal to zero. $\sqrt{54 t^{6}}$

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Problem 1312

妏, Simplify. $\sqrt{490}$

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Problem 1313

Simplify. Rewrite the expression in the form $y^{n}$ . $\frac{y^{-7}}{y^{-13}}=$ $\square$

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Problem 1314

$\log _{8}(12)$

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Problem 1315

10. Simplify: $\left(\frac{2 x^{-4}}{y^{-2} x}\right)^{-3}$ (a) $-\frac{6 x^{15}}{y^{6}}$ (b) $-\frac{8 x^{15}}{y^{6}}$ (c) $-\frac{6 y^{5}}{x^{4}}$ (d) $\frac{y^{5}}{8 x^{4}}$ (e) $\frac{x^{15}}{8 y^{6}}$

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Problem 1316

Math 140 Fall 2024 lass Quiz 3 (15 minutes)
Date: blems. Show your working in the space provided. ppression $\frac{y^{2}+10 y+21}{y^{2}+16 y+63}$ b) $-\frac{y^{2}+10 y+21}{y^{2}+16 y+63}$

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Problem 1317

$\frac{81-x^{2}}{x^{2}-81} \cdot \frac{4}{x^{2}-16 x+63} \cdot \frac{9 x^{3}+27 x^{2}-630 x}{-x-10}$

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Problem 1318

Add. $\begin{array}{l} \frac{4}{1+y}+\frac{9}{1+y} \\ \frac{4}{1+y}+\frac{9}{1+y}= \end{array}$ (Simplify your answer.)

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Problem 1319

$\frac{x^{2}}{9 x-36}-\frac{-x+20}{9 x-36}$

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Problem 1320

Write the English phrase as an algebraic expression. Then simplify the expression. Let $x$ represent the number. Eight times the product of negative six and a number.
What is the algebraic expression? $\square$ (Do not simplify.) What is the simplified expression? $\square$

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Problem 1321

Questlon 6 of 10 Which choice is equivalent to the expression below? $\sqrt{18}-\sqrt{2}$ A. $16 \sqrt{2}$ B. $\sqrt{16}$ C. 3 D. $2 \sqrt{2}$

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Problem 1322

$i^{65}$

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Problem 1323

$f(x)=\ln \left((3 x)\left(5^{2 x}\right)\right)$

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Problem 1324

$(3+7 i)+(-5+6 i)$

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Problem 1325

Simplify the following using exponential and logarithmic properties: $\log _{2} 48-\log _{2} 3=$ [ Select ]

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Problem 1326

8 Simplify this expression into fully factored form, showing your work. $a=3 \quad b=9 \quad c=3 \quad g=2 \quad h=-1 \quad m=9 \quad n=-1 \quad q=3 \quad r=1 \quad t=30 \quad v=10$ $\left(\frac{a x+b}{c x^{2}+g x+h}\right)\left(\frac{m x^{2}+n}{x+q}\right)\left(\frac{x+r}{t x+v}\right)$

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Problem 1327

ully simplify $6 f^{2}+3 f+2-f^{2}+f$

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Problem 1328

A. $(3+2 i)(4+3 i)$

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Problem 1329

Evaluate the factorial expression. $\frac{13!}{11!}$ $\frac{13!}{11!}=$ $\square$ (Simplify your answer.)

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Problem 1330

Simplify. Enter the result as a single logarithm with a coefficient of 1. To enter the log, click in the answer cell, then click on the small yellow arrow on the right. Then click the Functions tab to access the log. If needed, you can change the base. Using the keyboard, you can also enter $\log _{3}\left(\frac{x^{2}}{2}\right)$ as $\log _{-} 3\left(x^{\wedge} 2 / 2\right)$ . $\log _{4}\left(2 x^{4}\right)-\log _{4}\left(11 x^{2}\right)=$ $\square$

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Problem 1331

$-9+\sqrt{-49}=$

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Problem 1332

Find the exponential form for the complex number below $z=\frac{(1+i)^{6}(1+\sqrt{3} i)^{6}}{e^{(1+i)^{2}}}$

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Problem 1333

Fletore pune
3 Shpreh rrënjët e mëposhtme në formën $a \sqrt{b}$ , ku $a$ dhe $b$ janë numra natyrorë. (a) $\sqrt{12}=\sqrt{\ldots \ldots \ldots} \times \sqrt{3}=$ $\sqrt{3}$ $\qquad$ (b) $\sqrt{20}=\sqrt{4} \times \sqrt{\ldots \ldots \ldots . .}=$
Mendo dy numra, njëri prej tyre katror i plotë, të cilët kur i shumëzon japin numrin 12. (c) $\sqrt{48}=\sqrt{\ldots \ldots \ldots} \times \sqrt{\ldots \ldots \ldots}=$ $\qquad$ (d) $\sqrt{3} \times \sqrt{27}$ (e) $\sqrt{98}-\sqrt{18}$ $\qquad$ (f) $5 \sqrt{28}-\sqrt{63}$ $\qquad$

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Problem 1334

$\left(-5 x^{4}+6 x^{3}+x-12\right)+\left(4 x^{4}-15 x^{3}+2 x^{2}-3\right)=$

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Problem 1335

Simplify $\frac{15}{20}$ $\square$

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Problem 1336

What is $2\left(\log _{3} 8+\log _{3} z\right)-\log _{3}\left(3^{4}-7^{2}\right)$ written as a single logarithm? $\log _{3} 2 z$ $\log _{3} 2 z^{2}$ $\log _{3} \frac{z^{2}}{4}$ $\log _{3} \frac{64 z^{2}}{\frac{81}{49}}$

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Problem 1337

Factor the following expression completely: $y^{2}-2 y-80=$ $\square$

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Problem 1338

Factor the following expression completely: $4 w^{2}-44 w+112=$ $\square$

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Problem 1339

Factor the following expression completely: $5 x^{4}-65 x^{3}+200 x^{2}=$ $\square$

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Problem 1340

Factor: $x^{2}+11 x+28$

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Problem 1341

Factor $36 x^{2}-49$

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Problem 1342

Fill in the gaps to factorise this expression. $x^{2}+4 x=x\left(\_+\square\right)$

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Problem 1343

(A) $\ln \left(\frac{5}{4}\right)$
2. (4 points) Expand the following logarithmic expression as much as possible. $\log _{3}\left(\frac{9\left(x^{2}-16\right)}{\sqrt{x+25}}\right)$

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Problem 1344

$a-a$

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Problem 1345

Kuta Software - Infinite Algebra 1 Simplifying Radical Expressions Simplify. 1) $\sqrt{125 n}$

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Problem 1346

3) $\sqrt{512 k^{2}}$

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Problem 1347

4) $\sqrt{512 m^{3}}$

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Problem 1348

Apply the properties of operations to multiply. $\begin{array}{l} \frac{1}{8} x \cdot \frac{-4}{7} x \\ \frac{1}{8} x \cdot \frac{-4}{7} x= \end{array}$ $\square$

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Problem 1349

2. Write $32^{-\frac{2}{5}}$ without using exponents or radicals.

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Problem 1350

2. Add/Subtract using the proper (a) (2 Points) $-3 i+2-4 i+16-(4-8 i)$ $-15 i+22$ $i+14$ $-i+14$ $15 i-22$

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Problem 1351

10) $\sqrt{200 m^{4} n}$

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Problem 1352

Put the quadratic into vertex form and state the coordinates of the vertex. $y=x^{2}-6 x+21$

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Problem 1353

The partial work to simplify the expression $\sqrt{972}$ is shown. Complete the work. $\begin{aligned} \sqrt{972} & =\sqrt{\square} \cdot \sqrt{\square} \cdot \sqrt{3} \\ & =\square \cdot 3 \cdot \sqrt{3} \\ & =18 \sqrt{3} \end{aligned}$

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Problem 1354

12) $\sqrt{64 m^{3} n^{3}}$

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Problem 1355

$\frac{12 k^{2} m^{8}}{4 k^{5} m^{5}}$

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Problem 1356

$\left.\log _{4}\left(x^{3} y^{2}\right)^{2}+6 \log _{4} x^{2} y^{5}+\log _{4}\left(\frac{1}{x^{6} y^{2}}\right) d\right) 4 \log _{6} x^{2} y-\log _{6} x^{3} y^{5}-\log _{6} \sqrt[4]{x^{3} y^{8}}$

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Problem 1357

Write the expression as a single logarithm with coefficient 1 . Assume all variables represent positive real numbers. 5) $\frac{2}{9} \log _{n} 4 y+\frac{8}{7} \log _{n}\left(16 y^{2}\right)$ 5) $\qquad$ A) $\log _{n}\left(64 y^{9 / 10}\right)$ B) $\log _{n}\left(4^{39 / 20} y^{63 / 40}\right)$ C) $\log _{n}\left(4^{158 / 63} y^{158 / 63}\right)$ D) $\log _{n}\left(64 y^{39 / 40}\right)$

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Problem 1358

$\frac{3}{5}-0.4$

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Problem 1359

d $\frac{2 \sqrt{5}}{5 \sqrt{2}}-\frac{20}{\sqrt{10}}+\left(\frac{2 \sqrt{10}}{15}-\frac{30}{\sqrt{40}}\right)$ .

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Problem 1360

Factor the expression completely where $a \neq 1$ :
$4x^{2} - 6xy + 30y^{2}$

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Problem 1361

Question 3
Write the equation in exponential form. Assume that all constants are positive and not equal to 1. $\log _{z}(y)=p$

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Problem 1362

$\sqrt{27} \cdot 2 \sqrt{18}$

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Problem 1363

Simplify. Enter the result as a single logarithm with a coefficient of 1. $\log _{4}(11 x)+\log _{4}\left(6 x^{2}\right)=$ $\square$ Calculator
Check Answer

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Problem 1364

Factor $f(x)$ into linear factors given that $k$ is a zero of $f(x)$ . 7) $f(x)=x^{3}-48 x-128 ; k=-4$ (multiplicity 2)

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Problem 1365

Rewrite as sums or differences of logarithms. $\begin{array}{l} \log _{d}\left(x^{9} y^{4} z\right) \\ \log _{d}\left(x^{9} y^{4} z\right)= \end{array}$

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Problem 1366

Factor. $9 y^{2}+48 y+64$

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Problem 1367

Multiply. $(5 u+4 v+2)(2 u-6)$
Simplify your answer. $\square$

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Problem 1368

Factor by grouping. $5 y^{3}-6 y^{2}+25 y-30$

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Problem 1369

$\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{1.5 \times 10^{15} \mathrm{~Hz}}$

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Problem 1370

Express $\left(30^{2}\right)^{\frac{1}{3}}$ in simplest radical form.

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Problem 1371

$E=\left(6.626 \times 10^{-34} \mathrm{~s} .5\right)\left(6.00 \times 10^{11} \mathrm{~Hz}\right)$

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Problem 1372

Rewrite the following without an exponent. $\left(\frac{4}{9}\right)^{-1}$

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Problem 1373

$\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{5.20 \times 10^{-5} \mathrm{~cm}}$

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Problem 1374

Rewrite the complex number $5\left(\cos \left(\frac{\pi}{2}\right)+i \sin \left(\frac{\pi}{2}\right)\right)$ in $a+b i$ form $\square$ Question Help: Video
Submit Question

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Problem 1375

Express $12^{\frac{1}{2}}$ in simplest radical form.

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Problem 1376

Factor. $y^{2}-9$

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Problem 1377

Express $32^{\frac{3}{5}}$ in simplest radical form.

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Problem 1378

Use the properties of logarithms to expand the following expression. $\log \sqrt[3]{x^{7} y^{2} z}$
Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive. $\log \sqrt[3]{x^{7} y^{2} z}=$ $\square$

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Problem 1379

Let $f(x)=3 x-1$ and $g(x)=x^{2}+4$ Find $(f \circ g)(1)$
Then $(f \circ g)(1)=$ $\square$ (Simplify your answer.)

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Problem 1380

$\frac{16}{91.2}$

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Problem 1381

Fractions Writing an linproper fraction as a mixed number
Rewrite $\frac{31}{8}$ as a mixed number. $\square$

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Problem 1382

$\frac{w^{2}-11 w+24}{w^{2}-18 w+80} \cdot \frac{w^{2}-15 w+50}{w^{2}-9 w+20}$

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Problem 1383

A top swimmer would be able to swim across a 25-meter pool in about $\frac{1}{5}$ of a minute. How fast can a top swimmer go?
Simplify your answer and write it as a proper fraction, mixed number, or whole number. $\square$ meters per minute

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Problem 1384

$(6250)^{2}$

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Problem 1385

Ise the distributive property to remove $\left(5 z^{2}-2 z^{5}+5\right) 6 z^{3}$
Simplify your answer as much as possible

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Problem 1386

Factor the following expression. $18 w x^{3} y^{6}+24 w^{3} x^{8}$

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Problem 1387

Factor the following expression. $12 w^{8} x^{9}-24 w^{2} x^{2} y^{6}$

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Problem 1388

Rewrite the following equation in slope-intercept form. $13 x+12 y=-7$
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$ Snbmit

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Problem 1389

21. $\sqrt{\frac{121}{100}}$
22. $\sqrt{\frac{14}{7}}$
23. $\sqrt{\frac{18}{50}}$
24. $\sqrt{\frac{144}{36}}$
25. $-4 \sqrt{\frac{9}{16}}$ (21) (22) (23) (24)

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Problem 1390

Question 20 Save a
To simplify the expression $-4+\frac{120}{-2(-5)}-3$ , all four operations must be performed once. Describe the order in which the operations need to be performed. Then simplify the expression. (i) Instructions 100 of 100 words remaining $B \cong I \equiv \equiv \equiv I_{x} \sim$

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Problem 1391

$\arctan \left(\tan \left(\frac{4 \pi}{3}\right)\right)$

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Problem 1392

$\begin{array}{l}x=2, y=4, A=3, b=-2 \\ -2 x+4 y-4 A+b=\end{array}$

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Problem 1393

$\sin _{0}^{-1}\left(\sin \left(\frac{\pi}{4}\right)\right)$

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Problem 1394

c) $\frac{(10 x)^{-1} y^{3}}{15 x^{3} y^{-3}}$

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Problem 1395

4. $-3 \cdot\left(9-5^{2}\right)$

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Problem 1396

Specialists can determine the speed a vehicle was traveling from the length of its skid marks d and the coefficient of friction f . The formula for calculating the speed s is $\mathrm{s}=15.9 \sqrt{\mathrm{df}}$ . Rewrite the formula to solve for the length of the skid marks. $d=$ (Simplify your answer. Use integers or decimals for any numbers in the expression.)

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Problem 1397

$9 x y+21 x+3 y+7$

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Problem 1398

Factor the following polynomial. $5 x^{2}+5 x y-8 x-8 y$

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Problem 1399

Factor the following polynomial. $5 x^{2}+2 x y+20 x+8 y$

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Problem 1400

Factor. $125 s^{3}+1$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $125 \mathrm{~s}^{3}+1=$ $\square$ (Factor completely.) B. The polynomial is prime.

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1 ...11 12 13 14 15 16 17 ...56

Simplify

Problem 1301

11 Simplify the expression. (2 Points) (4n4−8n+4)−(8n2+4n4+1)\left(4 n^{4}-8 n+4\right)-\left(8 n^{2}+4 n^{4}+1\right)(4n4−8n+4)−(8n2+4n4+1) −8n2−8n+3-8 n^{2}-8 n+3−8n2−8n+3 8n4+16n+38 n^{4}+16 n+38n4+16n+3 −16n2+3-16 n^{2}+3−16n2+3

Problem 1302

d x2y3×x2y4x3y5\frac{x^{2} y^{3} \times x^{2} y^{4}}{x^{3} y^{5}}x3y5x2y3×x2y4​ f r4s7×r4s7Ac7\frac{r^{4} s^{7} \times r^{4} s^{7}}{A_{c}^{7}}Ac7​r4s7×r4s7​

Problem 1303

Find the partial fraction decomposition. −16x3+4x\frac{-16}{x^{3}+4 x}x3+4x−16​

Problem 1304

Problem 1305

Simplify (3+2)(3−2)(3+\sqrt{2})(3-\sqrt{2})(3+2​)(3−2​). a. 3123^{\frac{1}{2}}321​ c. 7 b. 12\frac{1}{2}21​ d. 6Please select the best answer from the choices provided A B C D Mark this and retum

Problem 1306

Simplify 0.0812\sqrt{0.08^{12}}0.0812​ a. (0.08)6(0.08)^{6}(0.08)6 c. (0.16)6(0.16)^{6}(0.16)6 b. (0.8)6(0.8)^{6}(0.8)6 d. (0.12)8(0.12)^{8}(0.12)8Please select the best answer from the choices provided A B C D

Problem 1307

Evaluate. 57(23)2+19\frac{5}{7}\left(\frac{2}{3}\right)^{2}+\frac{1}{9}75​(32​)2+91​Write your answer in simplest form.

Problem 1308

Evaluate. −19−(−415)-\frac{1}{9}-\left(-\frac{4}{15}\right)−91​−(−154​)Write your answer in simplest form.

Problem 1309

Rewrite the following without an exponent. 4−44^{-4}4−4

Problem 1310

76[8+6(b−1)]76[8+6(b-1)]76[8+6(b−1)]

Problem 1311

1) 敨, Simplify. Assume ttt is greater than or equal to zero. 54t6\sqrt{54 t^{6}}54t6​

Problem 1312

妏, Simplify. 490\sqrt{490}490​

Problem 1313

Simplify. Rewrite the expression in the form yny^{n}yn. y−7y−13=\frac{y^{-7}}{y^{-13}}=y−13y−7​= □\square□

Problem 1314

log⁡8(12)\log _{8}(12)log8​(12)

Problem 1315

Problem 1316

Math 140 Fall 2024 lass Quiz 3 (15 minutes)Date: blems. Show your working in the space provided. ppression y2+10y+21y2+16y+63\frac{y^{2}+10 y+21}{y^{2}+16 y+63}y2+16y+63y2+10y+21​ b) −y2+10y+21y2+16y+63-\frac{y^{2}+10 y+21}{y^{2}+16 y+63}−y2+16y+63y2+10y+21​

Problem 1317

81−x2x2−81⋅4x2−16x+63⋅9x3+27x2−630x−x−10\frac{81-x^{2}}{x^{2}-81} \cdot \frac{4}{x^{2}-16 x+63} \cdot \frac{9 x^{3}+27 x^{2}-630 x}{-x-10}x2−8181−x2​⋅x2−16x+634​⋅−x−109x3+27x2−630x​

Problem 1318

Add. 41+y+91+y41+y+91+y=\begin{array}{l} \frac{4}{1+y}+\frac{9}{1+y} \\ \frac{4}{1+y}+\frac{9}{1+y}= \end{array}1+y4​+1+y9​1+y4​+1+y9​=​ (Simplify your answer.)

Problem 1319

x29x−36−−x+209x−36\frac{x^{2}}{9 x-36}-\frac{-x+20}{9 x-36}9x−36x2​−9x−36−x+20​

Problem 1320

Write the English phrase as an algebraic expression. Then simplify the expression. Let xxx represent the number. Eight times the product of negative six and a number.What is the algebraic expression? □\square□ (Do not simplify.) What is the simplified expression? □\square□

Problem 1321

Questlon 6 of 10 Which choice is equivalent to the expression below? 18−2\sqrt{18}-\sqrt{2}18​−2​ A. 16216 \sqrt{2}162​ B. 16\sqrt{16}16​ C. 3 D. 222 \sqrt{2}22​

Problem 1322

i65i^{65}i65

Problem 1323

f(x)=ln⁡((3x)(52x))f(x)=\ln \left((3 x)\left(5^{2 x}\right)\right)f(x)=ln((3x)(52x))

Problem 1324

(3+7i)+(−5+6i)(3+7 i)+(-5+6 i)(3+7i)+(−5+6i)

Problem 1325

Simplify the following using exponential and logarithmic properties: log⁡248−log⁡23=\log _{2} 48-\log _{2} 3=log2​48−log2​3= [ Select ]

Problem 1326

Problem 1327

ully simplify 6f2+3f+2−f2+f6 f^{2}+3 f+2-f^{2}+f6f2+3f+2−f2+f

Problem 1328

A. (3+2i)(4+3i)(3+2 i)(4+3 i)(3+2i)(4+3i)

Problem 1329

Evaluate the factorial expression. 13!11!\frac{13!}{11!}11!13!​ 13!11!=\frac{13!}{11!}=11!13!​= □\square□ (Simplify your answer.)

Problem 1330

Problem 1331

−9+−49=-9+\sqrt{-49}=−9+−49​=

Problem 1332

Find the exponential form for the complex number below z=(1+i)6(1+3i)6e(1+i)2z=\frac{(1+i)^{6}(1+\sqrt{3} i)^{6}}{e^{(1+i)^{2}}}z=e(1+i)2(1+i)6(1+3​i)6​

Problem 1333

Problem 1334

(−5x4+6x3+x−12)+(4x4−15x3+2x2−3)=\left(-5 x^{4}+6 x^{3}+x-12\right)+\left(4 x^{4}-15 x^{3}+2 x^{2}-3\right)=(−5x4+6x3+x−12)+(4x4−15x3+2x2−3)=

Problem 1335

Simplify 1520\frac{15}{20}2015​ □\square□

Problem 1336

Problem 1337

Factor the following expression completely: y2−2y−80=y^{2}-2 y-80=y2−2y−80= □\square□

Problem 1338

Factor the following expression completely: 4w2−44w+112=4 w^{2}-44 w+112=4w2−44w+112= □\square□

Problem 1339

Factor the following expression completely: 5x4−65x3+200x2=5 x^{4}-65 x^{3}+200 x^{2}=5x4−65x3+200x2= □\square□

Problem 1340

Factor: x2+11x+28x^{2}+11 x+28x2+11x+28

Problem 1341

Factor 36x2−4936 x^{2}-4936x2−49

Problem 1342

Fill in the gaps to factorise this expression. x2+4x=x(_+□)x^{2}+4 x=x\left(\_+\square\right)x2+4x=x(_+□)

Problem 1343

11 Simplify the expression. (2 Points) $\left(4 n^{4}-8 n+4\right)-\left(8 n^{2}+4 n^{4}+1\right)$ $-8 n^{2}-8 n+3$ $8 n^{4}+16 n+3$ $-16 n^{2}+3$

d $\frac{x^{2} y^{3} \times x^{2} y^{4}}{x^{3} y^{5}}$ f $\frac{r^{4} s^{7} \times r^{4} s^{7}}{A_{c}^{7}}$

Find the partial fraction decomposition. $\frac{-16}{x^{3}+4 x}$

Simplify $(3+\sqrt{2})(3-\sqrt{2})$ . a. $3^{\frac{1}{2}}$ c. 7 b. $\frac{1}{2}$ d. 6
Please select the best answer from the choices provided A B C D Mark this and retum

Simplify $\sqrt{0.08^{12}}$ a. $(0.08)^{6}$ c. $(0.16)^{6}$ b. $(0.8)^{6}$ d. $(0.12)^{8}$
Please select the best answer from the choices provided A B C D

Evaluate. $\frac{5}{7}\left(\frac{2}{3}\right)^{2}+\frac{1}{9}$
Write your answer in simplest form.

Evaluate. $-\frac{1}{9}-\left(-\frac{4}{15}\right)$
Write your answer in simplest form.

Rewrite the following without an exponent. $4^{-4}$

$76[8+6(b-1)]$

1) 敨, Simplify. Assume $t$ is greater than or equal to zero. $\sqrt{54 t^{6}}$

妏, Simplify. $\sqrt{490}$

Simplify. Rewrite the expression in the form $y^{n}$ . $\frac{y^{-7}}{y^{-13}}=$ $\square$

$\log _{8}(12)$

Math 140 Fall 2024 lass Quiz 3 (15 minutes)
Date: blems. Show your working in the space provided. ppression $\frac{y^{2}+10 y+21}{y^{2}+16 y+63}$ b) $-\frac{y^{2}+10 y+21}{y^{2}+16 y+63}$

$\frac{81-x^{2}}{x^{2}-81} \cdot \frac{4}{x^{2}-16 x+63} \cdot \frac{9 x^{3}+27 x^{2}-630 x}{-x-10}$

Add. $\begin{array}{l} \frac{4}{1+y}+\frac{9}{1+y} \\ \frac{4}{1+y}+\frac{9}{1+y}= \end{array}$ (Simplify your answer.)

$\frac{x^{2}}{9 x-36}-\frac{-x+20}{9 x-36}$

Write the English phrase as an algebraic expression. Then simplify the expression. Let $x$ represent the number. Eight times the product of negative six and a number.
What is the algebraic expression? $\square$ (Do not simplify.) What is the simplified expression? $\square$

Questlon 6 of 10 Which choice is equivalent to the expression below? $\sqrt{18}-\sqrt{2}$ A. $16 \sqrt{2}$ B. $\sqrt{16}$ C. 3 D. $2 \sqrt{2}$

$i^{65}$

$f(x)=\ln \left((3 x)\left(5^{2 x}\right)\right)$

$(3+7 i)+(-5+6 i)$

Simplify the following using exponential and logarithmic properties: $\log _{2} 48-\log _{2} 3=$ [ Select ]

ully simplify $6 f^{2}+3 f+2-f^{2}+f$

A. $(3+2 i)(4+3 i)$

Evaluate the factorial expression. $\frac{13!}{11!}$ $\frac{13!}{11!}=$ $\square$ (Simplify your answer.)

$-9+\sqrt{-49}=$

Find the exponential form for the complex number below $z=\frac{(1+i)^{6}(1+\sqrt{3} i)^{6}}{e^{(1+i)^{2}}}$

$\left(-5 x^{4}+6 x^{3}+x-12\right)+\left(4 x^{4}-15 x^{3}+2 x^{2}-3\right)=$

Simplify $\frac{15}{20}$ $\square$

Factor the following expression completely: $y^{2}-2 y-80=$ $\square$

Factor the following expression completely: $4 w^{2}-44 w+112=$ $\square$

Factor the following expression completely: $5 x^{4}-65 x^{3}+200 x^{2}=$ $\square$

Factor: $x^{2}+11 x+28$

Factor $36 x^{2}-49$

Fill in the gaps to factorise this expression. $x^{2}+4 x=x\left(\_+\square\right)$

(A) $\ln \left(\frac{5}{4}\right)$
2. (4 points) Expand the following logarithmic expression as much as possible. $\log _{3}\left(\frac{9\left(x^{2}-16\right)}{\sqrt{x+25}}\right)$

$a-a$

Kuta Software - Infinite Algebra 1 Simplifying Radical Expressions Simplify. 1) $\sqrt{125 n}$

3) $\sqrt{512 k^{2}}$

4) $\sqrt{512 m^{3}}$

Apply the properties of operations to multiply. $\begin{array}{l} \frac{1}{8} x \cdot \frac{-4}{7} x \\ \frac{1}{8} x \cdot \frac{-4}{7} x= \end{array}$ $\square$

2. Write $32^{-\frac{2}{5}}$ without using exponents or radicals.

2. Add/Subtract using the proper (a) (2 Points) $-3 i+2-4 i+16-(4-8 i)$ $-15 i+22$ $i+14$ $-i+14$ $15 i-22$

10) $\sqrt{200 m^{4} n}$

Put the quadratic into vertex form and state the coordinates of the vertex. $y=x^{2}-6 x+21$

12) $\sqrt{64 m^{3} n^{3}}$

$\frac{12 k^{2} m^{8}}{4 k^{5} m^{5}}$

$\frac{3}{5}-0.4$

d $\frac{2 \sqrt{5}}{5 \sqrt{2}}-\frac{20}{\sqrt{10}}+\left(\frac{2 \sqrt{10}}{15}-\frac{30}{\sqrt{40}}\right)$ .

Factor the expression completely where $a \neq 1$ :
$4x^{2} - 6xy + 30y^{2}$

Question 3
Write the equation in exponential form. Assume that all constants are positive and not equal to 1. $\log _{z}(y)=p$

$\sqrt{27} \cdot 2 \sqrt{18}$

Simplify. Enter the result as a single logarithm with a coefficient of 1. $\log _{4}(11 x)+\log _{4}\left(6 x^{2}\right)=$ $\square$ Calculator
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Factor $f(x)$ into linear factors given that $k$ is a zero of $f(x)$ . 7) $f(x)=x^{3}-48 x-128 ; k=-4$ (multiplicity 2)

Rewrite as sums or differences of logarithms. $\begin{array}{l} \log _{d}\left(x^{9} y^{4} z\right) \\ \log _{d}\left(x^{9} y^{4} z\right)= \end{array}$

Factor. $9 y^{2}+48 y+64$

Multiply. $(5 u+4 v+2)(2 u-6)$
Simplify your answer. $\square$

Factor by grouping. $5 y^{3}-6 y^{2}+25 y-30$

$\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{1.5 \times 10^{15} \mathrm{~Hz}}$

Express $\left(30^{2}\right)^{\frac{1}{3}}$ in simplest radical form.

$E=\left(6.626 \times 10^{-34} \mathrm{~s} .5\right)\left(6.00 \times 10^{11} \mathrm{~Hz}\right)$

Rewrite the following without an exponent. $\left(\frac{4}{9}\right)^{-1}$

$\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{5.20 \times 10^{-5} \mathrm{~cm}}$

Rewrite the complex number $5\left(\cos \left(\frac{\pi}{2}\right)+i \sin \left(\frac{\pi}{2}\right)\right)$ in $a+b i$ form $\square$ Question Help: Video
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