Question

Simplify :${25}^{\frac{3}{2}}$

Answer 1

Given ${25}^{\frac{3}{2}}$

$\begin{array}{c}{25}^{\frac{3}{2}}={25}^{\frac{1}{2}\times 3}\\ ={\left({25}^{\frac{1}{2}}\right)}^3\left[\therefore {\left(a^m\right)}^n=a^{mn}\right]\\ =5^3\\ =125\end{array}$

Hence the simplified form of ${25}^{\frac{3}{2}}$ is $125$.