Simplify square root of 4x^3* square root of 9x

$\sqrt{4 x^{3}} \cdot \sqrt{9 x}$

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

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} x^{3}} \cdot \sqrt{9 x}$

Factor out $x^{2}$ .

$\sqrt{2^{2} (x^{2} x)} \cdot \sqrt{9 x}$

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

$\sqrt{{(2 x)}^{2} x} \cdot \sqrt{9 x}$

Pull terms out from under the radical.

$2 x \sqrt{x} \cdot \sqrt{9 x}$

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

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

Pull terms out from under the radical.

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

Multiply $2 x \sqrt{x} (3 \sqrt{x})$ .

Multiply $3$ by $2$ .

$6 x \sqrt{x} \sqrt{x}$

Raise $\sqrt{x}$ to the power of $1$ .

$6 x ({\sqrt{x}}^{1} \sqrt{x})$

Raise $\sqrt{x}$ to the power of $1$ .

$6 x ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$6 x {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$6 x {\sqrt{x}}^{2}$

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$6 x {(x^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$6 x \cdot x^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$6 x \cdot x^{1}$

Simplify.

$6 x \cdot x$

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

Move $x$ .

$6 (x \cdot x)$

Multiply $x$ by $x$ .

$6 x^{2}$