Evaluate fourth root of 81/16

$\sqrt[4]{\frac{81}{16}}$

Step 1

Rewrite $\sqrt[4]{\frac{81}{16}}$ as $\frac{\sqrt[4]{81}}{\sqrt[4]{16}}$ .

$\frac{\sqrt[4]{81}}{\sqrt[4]{16}}$

Step 2

Simplify the numerator.

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

$\frac{\sqrt[4]{3^{4}}}{\sqrt[4]{16}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3}{\sqrt[4]{16}}$

Step 3

Simplify the denominator.

Rewrite $16$ as $2^{4}$ .

$\frac{3}{\sqrt[4]{2^{4}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$