Simplify cube root of 8x^6* fourth root of 81x^12

$\sqrt[3]{8 x^{6}} \cdot \sqrt[4]{81 x^{12}}$

Step 1

Rewrite $8 x^{6}$ as ${(2 x^{2})}^{3}$ .

$\sqrt[3]{{(2 x^{2})}^{3}} \cdot \sqrt[4]{81 x^{12}}$

Step 2

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

$2 x^{2} \cdot \sqrt[4]{81 x^{12}}$

Step 3

Rewrite $81 x^{12}$ as ${(3 x^{3})}^{4}$ .

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

Step 4

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

$2 x^{2} \cdot (3 x^{3})$

Step 5

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x^{2} x^{3}$

Step 6

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$2 \cdot 3 (x^{3} x^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 3 x^{3 + 2}$

Add $3$ and $2$ .

$2 \cdot 3 x^{5}$

Step 7

Multiply $2$ by $3$ .

$6 x^{5}$