Algebra Examples

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

Step 1

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

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

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{\sqrt[4]{2^{4}}}{\sqrt[4]{81}}$

Step 2.2

Pull terms out from under the radical.

$\frac{| 2 |}{\sqrt[4]{81}}$

Step 2.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{2}{\sqrt[4]{81}}$

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

Pull terms out from under the radical.

$\frac{2}{| 3 |}$

Step 3.3

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

$\frac{2}{3}$