Simplify cube root of 27a^3* fourth root of 16b^8

$\sqrt[3]{27 a^{3}} \cdot \sqrt[4]{16 b^{8}}$

Step 1

Rewrite $27 a^{3}$ as ${(3 a)}^{3}$ .

$\sqrt[3]{{(3 a)}^{3}} \cdot \sqrt[4]{16 b^{8}}$

Step 2

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

$3 a \cdot \sqrt[4]{16 b^{8}}$

Step 3

Rewrite $16 b^{8}$ as ${(2 b^{2})}^{4}$ .

$3 a \cdot \sqrt[4]{{(2 b^{2})}^{4}}$

Step 4

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

$3 a \cdot (2 b^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$3 \cdot 2 a b^{2}$

Step 6

Multiply $3$ by $2$ .

$6 a b^{2}$