Simplify 4/( square root of 2a)

$\frac{4}{\sqrt{2 a}}$

Step 1

Multiply $\frac{4}{\sqrt{2 a}}$ by $\frac{\sqrt{2 a}}{\sqrt{2 a}}$ .

$\frac{4}{\sqrt{2 a}} \cdot \frac{\sqrt{2 a}}{\sqrt{2 a}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{4}{\sqrt{2 a}}$ by $\frac{\sqrt{2 a}}{\sqrt{2 a}}$ .

$\frac{4 \sqrt{2 a}}{\sqrt{2 a} \sqrt{2 a}}$

Raise $\sqrt{2 a}$ to the power of $1$ .

$\frac{4 \sqrt{2 a}}{{\sqrt{2 a}}^{1} \sqrt{2 a}}$

Raise $\sqrt{2 a}$ to the power of $1$ .

$\frac{4 \sqrt{2 a}}{{\sqrt{2 a}}^{1} {\sqrt{2 a}}^{1}}$

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

$\frac{4 \sqrt{2 a}}{{\sqrt{2 a}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 \sqrt{2 a}}{{\sqrt{2 a}}^{2}}$

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

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

$\frac{4 \sqrt{2 a}}{{({(2 a)}^{\frac{1}{2}})}^{2}}$

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

$\frac{4 \sqrt{2 a}}{{(2 a)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{4 \sqrt{2 a}}{{(2 a)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 \sqrt{2 a}}{{(2 a)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{4 \sqrt{2 a}}{{(2 a)}^{1}}$

Simplify.

$\frac{4 \sqrt{2 a}}{2 a}$

Step 3

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 \sqrt{2 a}$ .

$\frac{2 (2 \sqrt{2 a})}{2 a}$

Cancel the common factors.

Factor $2$ out of $2 a$ .

$\frac{2 (2 \sqrt{2 a})}{2 (a)}$

Cancel the common factor.

$\frac{2 (2 \sqrt{2 a})}{2 a}$

Rewrite the expression.

$\frac{2 \sqrt{2 a}}{a}$