Question

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

• A. $\frac{3}{5}$
• B. $\frac{3}{2}$
• C. $\frac{2}{5}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A)

$\frac{3}{5}$

${\left(\frac{625}{81}\right)}^{\frac{-1}{4}}$

$\Rightarrow {\left(\frac{625}{81}\right)}^{\frac{-1}{4}}={\left(\frac{81}{625}\right)}^{\frac{1}{4}}$

$\Rightarrow {\left[{\left(\frac{3}{5}\right)}^4\right]}^{\frac{1}{4}}$

$\Rightarrow \frac{3}{5}$

Hence, this is the answer.