Simplify 4/( square root of 63x)

$\frac{4}{\sqrt{63 x}}$

Step 1

Simplify the denominator.

Rewrite $63 x$ as $3^{2} \cdot (7 x)$ .

Factor $9$ out of $63$ .

$\frac{4}{\sqrt{9 (7) x}}$

Rewrite $9$ as $3^{2}$ .

$\frac{4}{\sqrt{3^{2} \cdot 7 x}}$

Add parentheses.

$\frac{4}{\sqrt{3^{2} \cdot (7 x)}}$

Pull terms out from under the radical.

$\frac{4}{3 \sqrt{7 x}}$

Step 2

Multiply $\frac{4}{3 \sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{4}{3 \sqrt{7 x}} \cdot \frac{\sqrt{7 x}}{\sqrt{7 x}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{4}{3 \sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{4 \sqrt{7 x}}{3 \sqrt{7 x} \sqrt{7 x}}$

Move $\sqrt{7 x}$ .

$\frac{4 \sqrt{7 x}}{3 (\sqrt{7 x} \sqrt{7 x})}$

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

$\frac{4 \sqrt{7 x}}{3 ({\sqrt{7 x}}^{1} \sqrt{7 x})}$

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

$\frac{4 \sqrt{7 x}}{3 ({\sqrt{7 x}}^{1} {\sqrt{7 x}}^{1})}$

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

$\frac{4 \sqrt{7 x}}{3 {\sqrt{7 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 \sqrt{7 x}}{3 {\sqrt{7 x}}^{2}}$

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

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

$\frac{4 \sqrt{7 x}}{3 {({(7 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{4 \sqrt{7 x}}{3 {(7 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{4 \sqrt{7 x}}{3 {(7 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 \sqrt{7 x}}{3 {(7 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{4 \sqrt{7 x}}{3 {(7 x)}^{1}}$

Simplify.

$\frac{4 \sqrt{7 x}}{3 (7 x)}$

Step 4

Multiply $3$ by $7$ .

$\frac{4 \sqrt{7 x}}{21 x}$

Simplify 4/( square root of 63x)

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