Question

Evaluate $5^{-4}\times (125{)}^{\frac{5}{3}}÷(25{)}^{\frac{-1}{2}}$

Answer 1

As given $\Rightarrow 5^{-4}\times (125{)}^{\frac{5}{3}}÷(25{)}^{\frac{-1}{2}}$

$\Rightarrow \frac{1}{5^4}\times {\left(5^3\right)}^{\frac{5}{3}}÷\frac{1}{{\left(5^2\right)}^{\frac{1}{2}}}$

$\Rightarrow \frac{1}{5^4}\times \left(5^{3.\frac{5}{3}}\right)÷\frac{1}{5^{2.\frac{1}{2}}}$

$\Rightarrow \frac{5^5}{5^4}÷\frac{1}{5}$

$\Rightarrow 5^{5-4}\times 5\Rightarrow 5\times 5=25$