Algebra Examples

$\frac{\sqrt[3]{135}}{\sqrt[3]{40}}$

Step 1

Combine $\sqrt[3]{135}$ and $\sqrt[3]{40}$ into a single radical.

$\sqrt[3]{\frac{135}{40}}$

Step 2

Cancel the common factor of $135$ and $40$ .

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Step 2.1

Factor $5$ out of $135$ .

$\sqrt[3]{\frac{5 (27)}{40}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $40$ .

$\sqrt[3]{\frac{5 \cdot 27}{5 \cdot 8}}$

Step 2.2.2

Cancel the common factor.

$\sqrt[3]{\frac{5 \cdot 27}{5 \cdot 8}}$

Step 2.2.3

Rewrite the expression.

$\sqrt[3]{\frac{27}{8}}$

Step 3

Rewrite $\sqrt[3]{\frac{27}{8}}$ as $\frac{\sqrt[3]{27}}{\sqrt[3]{8}}$ .

$\frac{\sqrt[3]{27}}{\sqrt[3]{8}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $27$ as $3^{3}$ .

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

Step 4.2

Pull terms out from under the radical.

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

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

Pull terms out from under the radical.

$\frac{3}{2}$