Algebra Examples

$\frac{8}{\sqrt[3]{16}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $16$ as $2^{3} \cdot 2$ .

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Step 1.1.1

Factor $8$ out of $16$ .

$\frac{8}{\sqrt[3]{8 (2)}}$

Step 1.1.2

Rewrite $8$ as $2^{3}$ .

$\frac{8}{\sqrt[3]{2^{3} \cdot 2}}$

Step 1.2

Pull terms out from under the radical.

$\frac{8}{2 \sqrt[3]{2}}$

Step 2

Cancel the common factor of $8$ and $2$ .

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Step 2.1

Factor $2$ out of $8$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 \sqrt[3]{2}$ .

$\frac{2 \cdot 4}{2 (\sqrt[3]{2})}$

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

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

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

Step 4.2

Raise $\sqrt[3]{2}$ to the power of $1$ .

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

Step 4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 4.4

Add $1$ and $2$ .

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

Step 4.5

Rewrite ${\sqrt[3]{2}}^{3}$ as $2$ .

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Step 4.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

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

Step 4.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.5.3

Combine $\frac{1}{3}$ and $3$ .

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

Step 4.5.4

Cancel the common factor of $3$ .

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Step 4.5.4.1

Cancel the common factor.

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

Step 4.5.4.2

Rewrite the expression.

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

Step 4.5.5

Evaluate the exponent.

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

Step 5

Cancel the common factor of $4$ and $2$ .

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Step 5.1

Factor $2$ out of $4 {\sqrt[3]{2}}^{2}$ .

$\frac{2 (2 {\sqrt[3]{2}}^{2})}{2}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2$ .

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

Step 5.2.2

Cancel the common factor.

$\frac{2 (2 {\sqrt[3]{2}}^{2})}{2 \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{2 {\sqrt[3]{2}}^{2}}{1}$

Step 5.2.4

Divide $2 {\sqrt[3]{2}}^{2}$ by $1$ .

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

Step 6

Rewrite ${\sqrt[3]{2}}^{2}$ as $\sqrt[3]{2^{2}}$ .

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

Step 7

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

$2 \sqrt[3]{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{4}$

Decimal Form:

$3.17480210 \dots$