Simplify ( cube root of 6* cube root of 36)/( cube root of 8)

$\frac{\sqrt[3]{6} \cdot \sqrt[3]{36}}{\sqrt[3]{8}}$

Step 1

Combine $\sqrt[3]{6}$ and $\sqrt[3]{8}$ into a single radical.

$\sqrt[3]{\frac{6}{8}} \cdot \sqrt[3]{36}$

Step 2

Combine using the product rule for radicals.

$\sqrt[3]{\frac{6}{8} \cdot 36}$

Step 3

Combine $\frac{6}{8}$ and $36$ .

$\sqrt[3]{\frac{6 \cdot 36}{8}}$

Step 4

Reduce the expression $\frac{6 \cdot 36}{8}$ by cancelling the common factors.

Factor $2$ out of $6 \cdot 36$ .

$\sqrt[3]{\frac{2 (3 \cdot 36)}{8}}$

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

Factor $4$ out of $3 \cdot 36$ .

$\sqrt[3]{\frac{4 (3 \cdot 9)}{4}}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\sqrt[3]{\frac{4 (3 \cdot 9)}{4 (1)}}$

Cancel the common factor.

$\sqrt[3]{\frac{4 (3 \cdot 9)}{4 \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{3 \cdot 9}{1}}$

Divide $3 \cdot 9$ by $1$ .

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

Step 6

Write the expression using exponents.

Multiply $3$ by $9$ .

$\sqrt[3]{27}$

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

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

Step 7

Pull terms out from under the radical, assuming real numbers.

$3$