((1)/(8))^(-(2)/(3)) What is the value of the given expression? Choose 1 answer: (A) -(1)/(12) (B) (1)/(4) (c) 4 (D) 12

Rephrasing the expression: First, let's rephrase the ＂What is the value of the expression ((1)/(8))^(-(2)/(3))?＂Understanding exponent properties: To solve the expression ((1)/(8))^(-(2)/(3)), we need to understand the properties of exponents. A negative exponent means that we take the reciprocal of the base. So, ((1)/(8))^(-(2)/(3)) is the same as (8/1)^((2)/(3)).Evaluating the base: Next, we need to evaluate (8/1)^((2)/(3)). The exponent (2/3) means that we take the cube root of the base and then square it. The cube root of 8 is 2, because 2^3 = 8.Finding the cube root: After finding the cube root of 8, we square the result to get the final answer. So, 2 squared is 4.Squaring the result: Therefore, the value of the given expression ((1)/(8))^(-(2)/(3)) is 4, which corresponds to choice (C).

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((1)/(8))^(-(2)/(3))
What is the value of the given expression?
Choose 1 answer:
(A)
-(1)/(12)
(B)
(1)/(4)
(c) 4
(D) 12

$\left(\frac{1}{8}\right)^{-\frac{2}{3}}$ $\newline$ What is the value of the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{1}{12}$ $\newline$ (B) $\frac{1}{4}$ $\newline$ (C) $4$ $\newline$ (D) $12$

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Algebra 1

Compare linear and exponential growth

Full solution

\left(\frac{1}{8}\right)^{-\frac{2}{3}}

\newline

What is the value of the given expression?

\newline

Choose

1

answer:

\newline

(A)

-\frac{1}{12}

\newline

(B)

\frac{1}{4}

\newline

(C)

4

\newline

(D)

12

Rephrasing the expression: First, let's rephrase the ＂What is the value of the expression $\left(\frac{1}{8}\right)^{-\frac{2}{3}}$ ?＂
Understanding exponent properties: To solve the expression $(\frac{1}{8})^{-\frac{2}{3}}$ , we need to understand the properties of exponents. A negative exponent means that we take the reciprocal of the base. So, $(\frac{1}{8})^{-\frac{2}{3}}$ is the same as $(\frac{8}{1})^{\frac{2}{3}}$ .
Evaluating the base: Next, we need to evaluate $(\frac{8}{1})^{(\frac{2}{3})}$ . The exponent $(\frac{2}{3})$ means that we take the cube root of the base and then square it. The cube root of $8$ is $2$ , because $2^3 = 8$ .
Finding the cube root: After finding the cube root of $8$ , we square the result to get the final answer. So, $2$ squared is $4$ .
Squaring the result: Therefore, the value of the given expression $\left(\frac{1}{8}\right)^{-\frac{2}{3}}$ is $4$ , which corresponds to choice (C).