Simplify 9/( square root of 3a)

$\frac{9}{\sqrt{3 a}}$

Step 1

Multiply $\frac{9}{\sqrt{3 a}}$ by $\frac{\sqrt{3 a}}{\sqrt{3 a}}$ .

$\frac{9}{\sqrt{3 a}} \cdot \frac{\sqrt{3 a}}{\sqrt{3 a}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{9}{\sqrt{3 a}}$ by $\frac{\sqrt{3 a}}{\sqrt{3 a}}$ .

$\frac{9 \sqrt{3 a}}{\sqrt{3 a} \sqrt{3 a}}$

Raise $\sqrt{3 a}$ to the power of $1$ .

$\frac{9 \sqrt{3 a}}{{\sqrt{3 a}}^{1} \sqrt{3 a}}$

Raise $\sqrt{3 a}$ to the power of $1$ .

$\frac{9 \sqrt{3 a}}{{\sqrt{3 a}}^{1} {\sqrt{3 a}}^{1}}$

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

$\frac{9 \sqrt{3 a}}{{\sqrt{3 a}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{9 \sqrt{3 a}}{{\sqrt{3 a}}^{2}}$

Rewrite ${\sqrt{3 a}}^{2}$ as $3 a$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 a}$ as ${(3 a)}^{\frac{1}{2}}$ .

$\frac{9 \sqrt{3 a}}{{({(3 a)}^{\frac{1}{2}})}^{2}}$

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

$\frac{9 \sqrt{3 a}}{{(3 a)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{9 \sqrt{3 a}}{{(3 a)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 \sqrt{3 a}}{{(3 a)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{9 \sqrt{3 a}}{{(3 a)}^{1}}$

Simplify.

$\frac{9 \sqrt{3 a}}{3 a}$

Step 3

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 \sqrt{3 a}$ .

$\frac{3 (3 \sqrt{3 a})}{3 a}$

Cancel the common factors.

Factor $3$ out of $3 a$ .

$\frac{3 (3 \sqrt{3 a})}{3 (a)}$

Cancel the common factor.

$\frac{3 (3 \sqrt{3 a})}{3 a}$

Rewrite the expression.

$\frac{3 \sqrt{3 a}}{a}$