Simplify x^3 square root of x^9

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

Step 1

Rewrite $x^{9}$ as ${(x^{4})}^{2} x$ .

Factor out $x^{8}$ .

$x^{3} \sqrt{x^{8} x}$

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

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

Step 2

Pull terms out from under the radical.

$x^{3} (x^{4} \sqrt{x})$

Step 3

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

$x^{4 + 3} \sqrt{x}$

Add $4$ and $3$ .

$x^{7} \sqrt{x}$