Question

Find value of ${(-\frac{1}{27})}^{-\frac{2}{3}}$.

Answer 1

Solution:- given

$={\left(\frac{-1}{27}\right)}^{\frac{-2}{3}}$

$={\left[{\left(\frac{-1}{27}\right)}^2\right]}^{\frac{-1}{3}}={\left(\frac{1}{{27}^2}\right)}^{\frac{-1}{3}}=\frac{1}{{\left(\frac{1}{{27}^2}\right)}^{\frac{1}{3}}}$

$=({27}^2{)}^{\frac{1}{3}}$

$=(3{)}^2=9(Ans)$