Simplify 4/( square root of 45x)

$\frac{4}{\sqrt{45 x}}$

Step 1

Simplify the denominator.

Rewrite $45 x$ as $3^{2} \cdot (5 x)$ .

Factor $9$ out of $45$ .

$\frac{4}{\sqrt{9 (5) x}}$

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

$\frac{4}{\sqrt{3^{2} \cdot 5 x}}$

Add parentheses.

$\frac{4}{\sqrt{3^{2} \cdot (5 x)}}$

Pull terms out from under the radical.

$\frac{4}{3 \sqrt{5 x}}$

Step 2

Multiply $\frac{4}{3 \sqrt{5 x}}$ by $\frac{\sqrt{5 x}}{\sqrt{5 x}}$ .

$\frac{4}{3 \sqrt{5 x}} \cdot \frac{\sqrt{5 x}}{\sqrt{5 x}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{4}{3 \sqrt{5 x}}$ by $\frac{\sqrt{5 x}}{\sqrt{5 x}}$ .

$\frac{4 \sqrt{5 x}}{3 \sqrt{5 x} \sqrt{5 x}}$

Move $\sqrt{5 x}$ .

$\frac{4 \sqrt{5 x}}{3 (\sqrt{5 x} \sqrt{5 x})}$

Raise $\sqrt{5 x}$ to the power of $1$ .

$\frac{4 \sqrt{5 x}}{3 ({\sqrt{5 x}}^{1} \sqrt{5 x})}$

Raise $\sqrt{5 x}$ to the power of $1$ .

$\frac{4 \sqrt{5 x}}{3 ({\sqrt{5 x}}^{1} {\sqrt{5 x}}^{1})}$

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

$\frac{4 \sqrt{5 x}}{3 {\sqrt{5 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 \sqrt{5 x}}{3 {\sqrt{5 x}}^{2}}$

Rewrite ${\sqrt{5 x}}^{2}$ as $5 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

$\frac{4 \sqrt{5 x}}{3 {({(5 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{4 \sqrt{5 x}}{3 {(5 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{4 \sqrt{5 x}}{3 {(5 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 \sqrt{5 x}}{3 {(5 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{4 \sqrt{5 x}}{3 {(5 x)}^{1}}$

Simplify.

$\frac{4 \sqrt{5 x}}{3 (5 x)}$

Step 4

Multiply $3$ by $5$ .

$\frac{4 \sqrt{5 x}}{15 x}$

Simplify 4/( square root of 45x)

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