Simplify x square root of 9x^3-2 square root of x^5

$x \sqrt{9 x^{3}} - 2 \sqrt{x^{5}}$

Simplify each term.

Rewrite $9 x^{3}$ as ${(3 x)}^{2} x$ .

Rewrite $9$ as $3^{2}$ .

$x \sqrt{3^{2} x^{3}} - 2 \sqrt{x^{5}}$

Factor out $x^{2}$ .

$x \sqrt{3^{2} (x^{2} x)} - 2 \sqrt{x^{5}}$

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

$x \sqrt{{(3 x)}^{2} x} - 2 \sqrt{x^{5}}$

Pull terms out from under the radical.

$x (3 x \sqrt{x}) - 2 \sqrt{x^{5}}$

Rewrite using the commutative property of multiplication.

$3 x (x \sqrt{x}) - 2 \sqrt{x^{5}}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) \sqrt{x} - 2 \sqrt{x^{5}}$

Multiply $x$ by $x$ .

$3 x^{2} \sqrt{x} - 2 \sqrt{x^{5}}$

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

Factor out $x^{4}$ .

$3 x^{2} \sqrt{x} - 2 \sqrt{x^{4} x}$

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

$3 x^{2} \sqrt{x} - 2 \sqrt{{(x^{2})}^{2} x}$

Pull terms out from under the radical.

$3 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x}$

Simplify by adding terms.

Subtract $2 x^{2} \sqrt{x}$ from $3 x^{2} \sqrt{x}$ .

$1 x^{2} \sqrt{x}$

Multiply $x^{2}$ by $1$ .

$x^{2} \sqrt{x}$