Basic Math Examples

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

Step 1

Multiply $\frac{4}{\sqrt[3]{36}}$ by $\frac{{\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{2}}$ .

$\frac{4}{\sqrt[3]{36}} \cdot \frac{{\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{2}}$

Step 2

Simplify terms.

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Step 2.1

Combine and simplify the denominator.

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Step 2.1.1

Multiply $\frac{4}{\sqrt[3]{36}}$ by $\frac{{\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{2}}$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{\sqrt[3]{36} {\sqrt[3]{36}}^{2}}$

Step 2.1.2

Raise $\sqrt[3]{36}$ to the power of $1$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{1} {\sqrt[3]{36}}^{2}}$

Step 2.1.3

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

$\frac{4 {\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{1 + 2}}$

Step 2.1.4

Add $1$ and $2$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{3}}$

Step 2.1.5

Rewrite ${\sqrt[3]{36}}^{3}$ as $36$ .

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Step 2.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{36}$ as $36^{\frac{1}{3}}$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{{(36^{\frac{1}{3}})}^{3}}$

Step 2.1.5.2

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

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{\frac{1}{3} \cdot 3}}$

Step 2.1.5.3

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

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{\frac{3}{3}}}$

Step 2.1.5.4

Cancel the common factor of $3$ .

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Step 2.1.5.4.1

Cancel the common factor.

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{\frac{3}{3}}}$

Step 2.1.5.4.2

Rewrite the expression.

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{1}}$

Step 2.1.5.5

Evaluate the exponent.

$\frac{4 {\sqrt[3]{36}}^{2}}{36}$

Step 2.2

Cancel the common factor of $4$ and $36$ .

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Step 2.2.1

Factor $4$ out of $4 {\sqrt[3]{36}}^{2}$ .

$\frac{4 ({\sqrt[3]{36}}^{2})}{36}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $4$ out of $36$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{4 \cdot 9}$

Step 2.2.2.2

Cancel the common factor.

$\frac{4 {\sqrt[3]{36}}^{2}}{4 \cdot 9}$

Step 2.2.2.3

Rewrite the expression.

$\frac{{\sqrt[3]{36}}^{2}}{9}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[3]{36}}^{2}$ as $\sqrt[3]{36^{2}}$ .

$\frac{\sqrt[3]{36^{2}}}{9}$

Step 3.2

Raise $36$ to the power of $2$ .

$\frac{\sqrt[3]{1296}}{9}$

Step 3.3

Rewrite $1296$ as $6^{3} \cdot 6$ .

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Step 3.3.1

Factor $216$ out of $1296$ .

$\frac{\sqrt[3]{216 (6)}}{9}$

Step 3.3.2

Rewrite $216$ as $6^{3}$ .

$\frac{\sqrt[3]{6^{3} \cdot 6}}{9}$

Step 3.4

Pull terms out from under the radical.

$\frac{6 \sqrt[3]{6}}{9}$

Step 4

Cancel the common factor of $6$ and $9$ .

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Step 4.1

Factor $3$ out of $6 \sqrt[3]{6}$ .

$\frac{3 (2 \sqrt[3]{6})}{9}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $9$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.21141372 \dots$