Question

Find the value $(512{)}^{\frac{-2}{9}}$

Answer 1

Given that

Let $a=(512{)}^{\frac{-2}{9}}$

$={\left(2^9\right)}^{\frac{-2}{9}}$

$=\left(2^{9\cdot \frac{-2}{9}}\right)$

$=2^{-2}$

$=\frac{1}{2^2}$

$a=\frac{1}{4}$

$(512{)}^{\frac{-2}{9}}=\frac{1}{4}$