Finite Math Examples

$\frac{4}{\sqrt[3]{13}}$

Step 1

Multiply $\frac{4}{\sqrt[3]{13}}$ by $\frac{{\sqrt[3]{13}}^{2}}{{\sqrt[3]{13}}^{2}}$ .

$\frac{4}{\sqrt[3]{13}} \cdot \frac{{\sqrt[3]{13}}^{2}}{{\sqrt[3]{13}}^{2}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{4}{\sqrt[3]{13}}$ by $\frac{{\sqrt[3]{13}}^{2}}{{\sqrt[3]{13}}^{2}}$ .

$\frac{4 {\sqrt[3]{13}}^{2}}{\sqrt[3]{13} {\sqrt[3]{13}}^{2}}$

Step 2.2

Raise $\sqrt[3]{13}$ to the power of $1$ .

$\frac{4 {\sqrt[3]{13}}^{2}}{{\sqrt[3]{13}}^{1} {\sqrt[3]{13}}^{2}}$

Step 2.3

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

$\frac{4 {\sqrt[3]{13}}^{2}}{{\sqrt[3]{13}}^{1 + 2}}$

Step 2.4

Add $1$ and $2$ .

$\frac{4 {\sqrt[3]{13}}^{2}}{{\sqrt[3]{13}}^{3}}$

Step 2.5

Rewrite ${\sqrt[3]{13}}^{3}$ as $13$ .

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Step 2.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{13}$ as $13^{\frac{1}{3}}$ .

$\frac{4 {\sqrt[3]{13}}^{2}}{{(13^{\frac{1}{3}})}^{3}}$

Step 2.5.2

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

$\frac{4 {\sqrt[3]{13}}^{2}}{13^{\frac{1}{3} \cdot 3}}$

Step 2.5.3

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

$\frac{4 {\sqrt[3]{13}}^{2}}{13^{\frac{3}{3}}}$

Step 2.5.4

Cancel the common factor of $3$ .

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Step 2.5.4.1

Cancel the common factor.

$\frac{4 {\sqrt[3]{13}}^{2}}{13^{\frac{3}{3}}}$

Step 2.5.4.2

Rewrite the expression.

$\frac{4 {\sqrt[3]{13}}^{2}}{13^{1}}$

Step 2.5.5

Evaluate the exponent.

$\frac{4 {\sqrt[3]{13}}^{2}}{13}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[3]{13}}^{2}$ as $\sqrt[3]{13^{2}}$ .

$\frac{4 \sqrt[3]{13^{2}}}{13}$

Step 3.2

Raise $13$ to the power of $2$ .

$\frac{4 \sqrt[3]{169}}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt[3]{169}}{13}$

Decimal Form:

$1.70116148 \dots$