Question

Evaluate the following expression ${\left(\frac{625}{81}\right)}^{-1/4}$

Answer 1

Consider the given expression,${\left(\frac{625}{81}\right)}^{\frac{-1}{4}}$

It is known that $625=5^4$ and $81=3^4$

${\left(\frac{625}{81}\right)}^{\frac{-1}{4}}={\left[{\left(\frac{5}{3}\right)}^4\right]}^{\frac{-1}{4}}={\left(\frac{5}{3}\right)}^{4\left(\frac{-1}{4}\right)}$

$={\left(\frac{5}{3}\right)}^{-1}=\frac{3}{5}$