Question

simplify the expression.
$8^{-\frac{4}{3}}$
simplify $8^{-\frac{4}{3}}$ completely. choose the correct answer below.
a. $\frac{1}{16}$
b. $-16$
c. $\frac{1}{(\sqrt3{8})^4}$
d. $sqrt3{8^{-4}}$

Explanation:

Step1: Rewrite negative exponent

$8^{-\frac{4}{3}} = \frac{1}{8^{\frac{4}{3}}}$

Step2: Rewrite rational exponent

$\frac{1}{8^{\frac{4}{3}}} = \frac{1}{(\sqrt[3]{8})^4}$

Step3: Evaluate cube root of 8

$\sqrt[3]{8} = 2$, so $\frac{1}{2^4}$

Step4: Calculate power of 2

$2^4 = 16$, so $\frac{1}{16}$

Answer:

A. $\frac{1}{16}$