Simplify 1/( square root of 45z)

$\frac{1}{\sqrt{45 z}}$

Step 1

Simplify the denominator.

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

Factor $9$ out of $45$ .

$\frac{1}{\sqrt{9 (5) z}}$

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

$\frac{1}{\sqrt{3^{2} \cdot 5 z}}$

Add parentheses.

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

Pull terms out from under the radical.

$\frac{1}{3 \sqrt{5 z}}$

Step 2

Multiply $\frac{1}{3 \sqrt{5 z}}$ by $\frac{\sqrt{5 z}}{\sqrt{5 z}}$ .

$\frac{1}{3 \sqrt{5 z}} \cdot \frac{\sqrt{5 z}}{\sqrt{5 z}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{1}{3 \sqrt{5 z}}$ by $\frac{\sqrt{5 z}}{\sqrt{5 z}}$ .

$\frac{\sqrt{5 z}}{3 \sqrt{5 z} \sqrt{5 z}}$

Move $\sqrt{5 z}$ .

$\frac{\sqrt{5 z}}{3 (\sqrt{5 z} \sqrt{5 z})}$

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

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

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

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

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

$\frac{\sqrt{5 z}}{3 {\sqrt{5 z}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{5 z}}{3 {\sqrt{5 z}}^{2}}$

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{\sqrt{5 z}}{3 (5 z)}$

Step 4

Multiply $3$ by $5$ .

$\frac{\sqrt{5 z}}{15 z}$

Simplify 1/( square root of 45z)

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