Simplify the Radical Expression ( eighth root of 81)/( sixth root of 3)

$\frac{\sqrt[8]{81}}{\sqrt[6]{3}}$

Rewrite $81$ as $3^{4}$ .

$\frac{\sqrt[8]{3^{4}}}{\sqrt[6]{3}}$

Rewrite $\sqrt[8]{3^{4}}$ as $\sqrt{\sqrt[4]{3^{4}}}$ .

$\frac{\sqrt{\sqrt[4]{3^{4}}}}{\sqrt[6]{3}}$

Pull terms out from under the radical.

$\frac{\sqrt{| 3 |}}{\sqrt[6]{3}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{\sqrt{3}}{\sqrt[6]{3}}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{\sqrt[6]{3}}$

Decimal Form:

$1.44224957 \dots$