Simplify the Radical Expression ( cube root of 6* cube root of 72)/( cube root of 2)

$\frac{\sqrt[3]{6} \cdot \sqrt[3]{72}}{\sqrt[3]{2}}$

Step 1

Combine $\sqrt[3]{6}$ and $\sqrt[3]{2}$ into a single radical.

$\sqrt[3]{\frac{6}{2}} \cdot \sqrt[3]{72}$

Step 2

Combine using the product rule for radicals.

$\sqrt[3]{\frac{6}{2} \cdot 72}$

Step 3

Combine $\frac{6}{2}$ and $72$ .

$\sqrt[3]{\frac{6 \cdot 72}{2}}$

Step 4

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{6 \cdot 72}{2}$ by cancelling the common factors.

Factor $2$ out of $6 \cdot 72$ .

$\sqrt[3]{\frac{2 (3 \cdot 72)}{2}}$

Factor $2$ out of $2$ .

$\sqrt[3]{\frac{2 (3 \cdot 72)}{2 (1)}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (3 \cdot 72)}{2 \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{3 \cdot 72}{1}}$

Divide $3 \cdot 72$ by $1$ .

$\sqrt[3]{3 \cdot 72}$

Step 5

Multiply $3$ by $72$ .

$\sqrt[3]{216}$

Step 6

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

$\sqrt[3]{6^{3}}$

Step 7

Pull terms out from under the radical.

$6$