Math / Algebra

Question8. $w^{-7}=$ $\qquad$ tive exponent. (Example 3)
10. $\frac{1}{12^{2}}=$ $\qquad$
12. $\frac{1}{6^{4}}=$ $\qquad$

Studdy Solution

STEP 1

1. We are asked to simplify expressions involving negative exponents and fractions.
2. We will convert negative exponents to positive exponents.
3. We will evaluate the fractions by calculating the powers.

STEP 2

1. Simplify the expression with a negative exponent $w^{-7}$ .
2. Simplify the expression $\frac{1}{12^2}$ .
3. Simplify the expression $\frac{1}{6^4}$ .

STEP 3

Convert the negative exponent to a positive exponent by using the property $a^{-n} = \frac{1}{a^n}$ .
$w^{-7} = \frac{1}{w^7}$

STEP 4

Calculate the power in the denominator:
$12^2 = 144$
Thus,
$\frac{1}{12^2} = \frac{1}{144}$

STEP 5

Calculate the power in the denominator:
$6^4 = 6 \times 6 \times 6 \times 6 = 1296$
Thus,
$\frac{1}{6^4} = \frac{1}{1296}$

Was this helpful?

Question8. $w^{-7}=$ $\qquad$ tive exponent. (Example 3)
10. $\frac{1}{12^{2}}=$ $\qquad$
12. $\frac{1}{6^{4}}=$ $\qquad$

Studdy Solution

STEP 1

1. We are asked to simplify expressions involving negative exponents and fractions.
2. We will convert negative exponents to positive exponents.
3. We will evaluate the fractions by calculating the powers.

STEP 2

1. Simplify the expression with a negative exponent $w^{-7}$ .
2. Simplify the expression $\frac{1}{12^2}$ .
3. Simplify the expression $\frac{1}{6^4}$ .

STEP 3

Convert the negative exponent to a positive exponent by using the property $a^{-n} = \frac{1}{a^n}$ .
$w^{-7} = \frac{1}{w^7}$

STEP 4

Calculate the power in the denominator:
$12^2 = 144$
Thus,
$\frac{1}{12^2} = \frac{1}{144}$

STEP 5

Calculate the power in the denominator:
$6^4 = 6 \times 6 \times 6 \times 6 = 1296$
Thus,
$\frac{1}{6^4} = \frac{1}{1296}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question8. w−7=w^{-7}=w−7= \qquad tive exponent. (Example 3)10. 1122=\frac{1}{12^{2}}=1221​= \qquad12. 164=\frac{1}{6^{4}}=641​= \qquad

Studdy Solution

STEP 1

1. We are asked to simplify expressions involving negative exponents and fractions.2. We will convert negative exponents to positive exponents.3. We will evaluate the fractions by calculating the powers.

STEP 2

1. Simplify the expression with a negative exponent w−7 w^{-7} w−7.2. Simplify the expression 1122\frac{1}{12^2}1221​.3. Simplify the expression 164\frac{1}{6^4}641​.

STEP 3

Convert the negative exponent to a positive exponent by using the property a−n=1an a^{-n} = \frac{1}{a^n} a−n=an1​.w−7=1w7 w^{-7} = \frac{1}{w^7} w−7=w71​

STEP 4

Calculate the power in the denominator:122=144 12^2 = 144 122=144Thus, 1122=1144 \frac{1}{12^2} = \frac{1}{144} 1221​=1441​

STEP 5

Calculate the power in the denominator:64=6×6×6×6=1296 6^4 = 6 \times 6 \times 6 \times 6 = 1296 64=6×6×6×6=1296Thus, 164=11296 \frac{1}{6^4} = \frac{1}{1296} 641​=12961​

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question8. $w^{-7}=$ $\qquad$ tive exponent. (Example 3)
10. $\frac{1}{12^{2}}=$ $\qquad$
12. $\frac{1}{6^{4}}=$ $\qquad$

1. We are asked to simplify expressions involving negative exponents and fractions.
2. We will convert negative exponents to positive exponents.
3. We will evaluate the fractions by calculating the powers.

1. Simplify the expression with a negative exponent $w^{-7}$ .
2. Simplify the expression $\frac{1}{12^2}$ .
3. Simplify the expression $\frac{1}{6^4}$ .

Convert the negative exponent to a positive exponent by using the property $a^{-n} = \frac{1}{a^n}$ .
$w^{-7} = \frac{1}{w^7}$

Calculate the power in the denominator:
$12^2 = 144$
Thus,
$\frac{1}{12^2} = \frac{1}{144}$

Calculate the power in the denominator:
$6^4 = 6 \times 6 \times 6 \times 6 = 1296$
Thus,
$\frac{1}{6^4} = \frac{1}{1296}$