Question

The value of ${\left[{\left(\sqrt[5]{5125}\right)}^{-2}\right]}^{-\frac{5}{3}}$.

• A. $5$
• B. $25$
• C. $\sqrt{5}$
• D. none of these

Answer 1

The correct option is B $25$

Now,

Let $a={\left[{\left(\sqrt[5]{5125}\right)}^{-2}\right]}^{-\frac{5}{3}}$

$={\left[\right(125{)}^{\frac{1}{5}}]}^{\frac{10}{3}}$

$={\left[\right(125\left)\right]}^{\frac{2}{3}}$

$={\left[\right(5^3\left)\right]}^{\frac{2}{3}}$

$=5^2$

$a=25$.

$\therefore {\left[{\left(\sqrt[5]{5125}\right)}^{-2}\right]}^{-\frac{5}{3}}=25$