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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

(18)−23 \left(\frac{1}{8}\right)^{-\frac{2}{3}} \newlineWhat is the value of the given expression?\newlineChoose 11 answer:\newline(A) −112 -\frac{1}{12} \newline(B) 14 \frac{1}{4} \newline(C) 44\newline(D) 1212

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Full solution

Q. (18)−23 \left(\frac{1}{8}\right)^{-\frac{2}{3}} \newlineWhat is the value of the given expression?\newlineChoose 11 answer:\newline(A) −112 -\frac{1}{12} \newline(B) 14 \frac{1}{4} \newline(C) 44\newline(D) 1212
  1. Rephrasing the expression: First, let's rephrase the ＂What is the value of the expression (18)−23\left(\frac{1}{8}\right)^{-\frac{2}{3}}?＂
  2. Understanding exponent properties: To solve the expression (18)−23(\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, (18)−23(\frac{1}{8})^{-\frac{2}{3}} is the same as (81)23(\frac{8}{1})^{\frac{2}{3}}.
  3. Evaluating the base: Next, we need to evaluate (81)(23)(\frac{8}{1})^{(\frac{2}{3})}. The exponent (23)(\frac{2}{3}) means that we take the cube root of the base and then square it. The cube root of 88 is 22, because 23=82^3 = 8.
  4. Finding the cube root: After finding the cube root of 88, we square the result to get the final answer. So, 22 squared is 44.
  5. Squaring the result: Therefore, the value of the given expression (18)−23\left(\frac{1}{8}\right)^{-\frac{2}{3}} is 44, which corresponds to choice (C).

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