How do we write (sqrt7)^3 in exponential form?

Jul 20, 2016

${\left(\sqrt{7}\right)}^{3} = {7}^{\frac{3}{2}}$

Explanation:

To write ${\left(\sqrt{7}\right)}^{3}$ in exponential form, one needs two identities - $\sqrt[n]{a} = {a}^{\frac{1}{n}}$ and (a^m)^n=a^((m×n)) which is true for all rational $m$ and $n$.

Hence, ${\left(\sqrt{7}\right)}^{3}$

= ${\left({7}^{\frac{1}{2}}\right)}^{3}$

= 7^((1/2×3))

= ${7}^{\frac{3}{2}}$