Finite Math Examples

${(\sqrt[4]{- 16})}^{3}$

Step 1

Rewrite $- 16$ as $2^{4} \cdot - 1$ .

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Step 1.1

Factor $16$ out of $- 16$ .

${\sqrt[4]{16 (- 1)}}^{3}$

Step 1.2

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

${\sqrt[4]{2^{4} \cdot - 1}}^{3}$

Step 2

Pull terms out from under the radical.

${(2 \sqrt[4]{- 1})}^{3}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $2 \sqrt[4]{- 1}$ .

$2^{3} {\sqrt[4]{- 1}}^{3}$

Step 3.2

Raise $2$ to the power of $3$ .

$8 {\sqrt[4]{- 1}}^{3}$

Step 4

Rewrite ${\sqrt[4]{- 1}}^{3}$ as $\sqrt[4]{{(- 1)}^{3}}$ .

$8 \sqrt[4]{{(- 1)}^{3}}$

Step 5

Raise $- 1$ to the power of $3$ .

$8 \sqrt[4]{- 1}$