Question

How do you write the expression $6^{\frac{3}{2}}$ in radical form?

Answer 1

Convert into radical form

To convert from the exponential form into the radical form, we use the identity,

${\mathbf{c}}^{\frac{\mathbf{m}}{\mathbf{n}}}\mathit{=}\sqrt[\mathbf{n}]{{\mathbf{c}}^{\mathbf{m}}}\mathit{,}\mathit{}\mathbf{n}\mathbf{>}\mathbf{0}$

Here,

$c=6$, $m=3$ and $n=2$'

Thus,

$6^{\frac{3}{2}}=\sqrt[2]{6^3}$

Therefore, $6^{\frac{3}{2}}$ in radical form is $\sqrt[2]{6^3}$.