Simplify ( square root of 45x^9)/( square root of 9)

$\frac{\sqrt{45 x^{9}}}{\sqrt{9}}$

Combine $\sqrt{45 x^{9}}$ and $\sqrt{9}$ into a single radical.

$\sqrt{\frac{45 x^{9}}{9}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{45 x^{9}}{9}$ by cancelling the common factors.

Factor $9$ out of $45 x^{9}$ .

$\sqrt{\frac{9 (5 x^{9})}{9}}$

Factor $9$ out of $9$ .

$\sqrt{\frac{9 (5 x^{9})}{9 (1)}}$

Cancel the common factor.

$\sqrt{\frac{9 (5 x^{9})}{9 \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{5 x^{9}}{1}}$

Divide $5 x^{9}$ by $1$ .

$\sqrt{5 x^{9}}$

Rewrite $5 x^{9}$ as ${({(x^{2})}^{2})}^{2} \cdot (5 x)$ .

Factor out $x^{8}$ .

$\sqrt{5 (x^{8} x)}$

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

$\sqrt{5 ({(x^{4})}^{2} x)}$

Reorder $5$ and ${(x^{4})}^{2}$ .

$\sqrt{{(x^{4})}^{2} \cdot 5 x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply the exponents in ${(x^{2})}^{2}$ .

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

$x^{2 \cdot 2} \sqrt{5 x}$

Multiply $2$ by $2$ .

$x^{4} \sqrt{5 x}$