Question

Find the value of ${\left(243\right)}^{\frac{1}{5}}$

Answer 1

Compute the required value

We know that, $243=3^5$

$$\begin{gathered} \therefore {\left(243\right)}^{\frac{1}{5}}={\left(3^5\right)}^{\frac{1}{5}} \\ ={\left(3\right)}^{5\times \frac{1}{5}}\left[\because {\left(a^m\right)}^n=a^{m\times n}\right] \\ =3^1 \\ \Rightarrow {\left(243\right)}^{\frac{1}{5}}=3 \end{gathered}$$

Hence, the value of ${\left(243\right)}^{\frac{1}{5}}$ is $3$