Question

Simplify :${81}^{\frac{1}{4}}$

Answer 1

Simplify ${81}^{\frac{1}{4}}$:

$\begin{array}{c}{81}^{\frac{1}{4}}={81}^{\frac{1}{2}\times \frac{1}{2}}\\ ={\left({81}^{\frac{1}{2}}\right)}^{\frac{1}{2}}\left[\because {\left(a^m\right)}^n=a^{mn}\right]\\ =9^{\frac{1}{2}}\left[\because {81}^{\frac{1}{2}}={\left(9^2\right)}^{\frac{1}{2}}=9\right]\\ =3\mathbf{}\left[\because 9^{\frac{1}{2}}=3\right]\end{array}$

Hence the simplified form of ${81}^{\frac{1}{4}}$ is $3$.