Simplify the Radical Expression ( cube root of 135)/( cube root of 40)

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

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 $40$ .

Factor $5$ out of $135$ .

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

Cancel the common factors.

Factor $5$ out of $40$ .

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

Cancel the common factor.

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

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.

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

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

Pull terms out from under the radical.

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

Step 5

Simplify the denominator.

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

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

Pull terms out from under the radical.

$\frac{3}{2}$