Pre-Algebra Examples

$\frac{\sqrt[3]{4}}{\sqrt[3]{6}} \cdot \frac{\sqrt[3]{36}}{\sqrt[3]{36}}$

Step 1

Cancel the common factor of $\sqrt[3]{36}$ .

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Step 1.1

Cancel the common factor.

$\frac{\sqrt[3]{4}}{\sqrt[3]{6}} \cdot \frac{\sqrt[3]{36}}{\sqrt[3]{36}}$

Step 1.2

Rewrite the expression.

$\frac{\sqrt[3]{4}}{\sqrt[3]{6}} \cdot 1$

Step 2

Multiply $\frac{\sqrt[3]{4}}{\sqrt[3]{6}}$ by $1$ .

$\frac{\sqrt[3]{4}}{\sqrt[3]{6}}$

Step 3

Combine $\sqrt[3]{4}$ and $\sqrt[3]{6}$ into a single radical.

$\sqrt[3]{\frac{4}{6}}$

Step 4

Cancel the common factor of $4$ and $6$ .

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Step 4.1

Factor $2$ out of $4$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $6$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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

Step 6

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

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

Step 7

Combine and simplify the denominator.

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Step 7.1

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

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

Step 7.2

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

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

Step 7.3

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

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

Step 7.4

Add $1$ and $2$ .

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

Step 7.5

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

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Step 7.5.1

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

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

Step 7.5.2

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

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

Step 7.5.3

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

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

Step 7.5.4

Cancel the common factor of $3$ .

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Step 7.5.4.1

Cancel the common factor.

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

Step 7.5.4.2

Rewrite the expression.

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

Step 7.5.5

Evaluate the exponent.

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

Step 8

Simplify the numerator.

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Step 8.1

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

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

Step 8.2

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

$\frac{\sqrt[3]{2} \sqrt[3]{9}}{3}$

Step 9

Simplify the numerator.

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Step 9.1

Combine using the product rule for radicals.

$\frac{\sqrt[3]{2 \cdot 9}}{3}$

Step 9.2

Multiply $2$ by $9$ .

$\frac{\sqrt[3]{18}}{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[3]{18}}{3}$

Decimal Form:

$0.87358046 \dots$