Algebra Examples

$\frac{\sqrt[3]{6}}{\sqrt[3]{5}}$

Step 1

Multiply to rationalize the numerator.

$\frac{\sqrt[3]{6} {\sqrt[3]{6}}^{2}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2

Simplify.

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Step 2.1

Raise $\sqrt[3]{6}$ to the power of $1$ .

$\frac{{\sqrt[3]{6}}^{1} {\sqrt[3]{6}}^{2}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.2

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

$\frac{{\sqrt[3]{6}}^{1 + 2}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.3

Add $1$ and $2$ .

$\frac{{\sqrt[3]{6}}^{3}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.4

Rewrite ${\sqrt[3]{6}}^{3}$ as $6$ .

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Step 2.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6}$ as $6^{\frac{1}{3}}$ .

$\frac{{(6^{\frac{1}{3}})}^{3}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.4.2

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

$\frac{6^{\frac{1}{3} \cdot 3}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.4.3

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

$\frac{6^{\frac{3}{3}}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.4.4

Cancel the common factor of $3$ .

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Step 2.4.4.1

Cancel the common factor.

$\frac{6^{\frac{3}{3}}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.4.4.2

Rewrite the expression.

$\frac{6^{1}}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.4.5

Evaluate the exponent.

$\frac{6}{\sqrt[3]{5} {\sqrt[3]{6}}^{2}}$

Step 2.5

Start simplifying.

$\frac{6}{\sqrt[3]{5} \sqrt[3]{6^{2}}}$

Step 2.6

Combine using the product rule for radicals.

$\frac{6}{\sqrt[3]{5 \cdot 6^{2}}}$

Step 2.7

Raise $6$ to the power of $2$ .

$\frac{6}{\sqrt[3]{5 \cdot 36}}$

Step 2.8

Multiply $5$ by $36$ .

$\frac{6}{\sqrt[3]{180}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{\sqrt[3]{180}}$

Decimal Form:

$1.06265856 \dots$