Question

The value of ${512}^{\frac{-2}{9}}$ is

• A. $\frac{1}{2}$
• B. $2$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

Answer: (D)

$\frac{1}{4}$

$\begin{array}{cc}{\left(512\right)}^{-\frac{2}{9}}& ={\left(2^9\right)}^{-\frac{2}{9}}\\ & =2^{9\times \frac{-2}{9}}\because \left[\right(a^b{)}^c=a^{bc}]\\ & =2^{-2}\\ & =\frac{1}{4}\end{array}$

Hence, option $D$ is correct.