Simplify square root of 36x^2* fourth root of 81x^8

$\sqrt{36 x^{2}} \cdot \sqrt[4]{81 x^{8}}$

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

$\sqrt{{(6 x)}^{2}} \cdot \sqrt[4]{81 x^{8}}$

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

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

Rewrite $81 x^{8}$ as ${(3 x^{2})}^{4}$ .

$6 x \cdot \sqrt[4]{{(3 x^{2})}^{4}}$

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

$6 x \cdot (3 x^{2})$

Rewrite using the commutative property of multiplication.

$6 \cdot 3 x \cdot x^{2}$

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

Move $x^{2}$ .

$6 \cdot 3 (x^{2} x)$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$6 \cdot 3 (x^{2} x^{1})$

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

$6 \cdot 3 x^{2 + 1}$

Add $2$ and $1$ .

$6 \cdot 3 x^{3}$

Multiply $6$ by $3$ .

$18 x^{3}$