Simplify 5/( square root of 7x)

$\frac{5}{\sqrt{7 x}}$

Step 1

Multiply $\frac{5}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{5}{\sqrt{7 x}} \cdot \frac{\sqrt{7 x}}{\sqrt{7 x}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{5}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{5 \sqrt{7 x}}{\sqrt{7 x} \sqrt{7 x}}$

Raise $\sqrt{7 x}$ to the power of $1$ .

$\frac{5 \sqrt{7 x}}{{\sqrt{7 x}}^{1} \sqrt{7 x}}$

Raise $\sqrt{7 x}$ to the power of $1$ .

$\frac{5 \sqrt{7 x}}{{\sqrt{7 x}}^{1} {\sqrt{7 x}}^{1}}$

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

$\frac{5 \sqrt{7 x}}{{\sqrt{7 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \sqrt{7 x}}{{\sqrt{7 x}}^{2}}$

Rewrite ${\sqrt{7 x}}^{2}$ as $7 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x}$ as ${(7 x)}^{\frac{1}{2}}$ .

$\frac{5 \sqrt{7 x}}{{({(7 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{5 \sqrt{7 x}}{{(7 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 \sqrt{7 x}}{{(7 x)}^{1}}$

Simplify.

$\frac{5 \sqrt{7 x}}{7 x}$