Simplify square root of (18^2)/(z^3)

$\sqrt{\frac{18^{2}}{z^{3}}}$

Step 1

Raise $18$ to the power of $2$ .

$\sqrt{\frac{324}{z^{3}}}$

Step 2

Rewrite $\frac{324}{z^{3}}$ as ${(\frac{18}{z})}^{2} \frac{1}{z}$ .

Factor the perfect power $18^{2}$ out of $324$ .

$\sqrt{\frac{18^{2} \cdot 1}{z^{3}}}$

Factor the perfect power $z^{2}$ out of $z^{3}$ .

$\sqrt{\frac{18^{2} \cdot 1}{z^{2} z}}$

Rearrange the fraction $\frac{18^{2} \cdot 1}{z^{2} z}$ .

$\sqrt{{(\frac{18}{z})}^{2} \frac{1}{z}}$

Step 3

Pull terms out from under the radical.

$\frac{18}{z} \sqrt{\frac{1}{z}}$

Step 4

Rewrite $\sqrt{\frac{1}{z}}$ as $\frac{\sqrt{1}}{\sqrt{z}}$ .

$\frac{18}{z} \cdot \frac{\sqrt{1}}{\sqrt{z}}$

Step 5

Any root of $1$ is $1$ .

$\frac{18}{z} \cdot \frac{1}{\sqrt{z}}$

Step 6

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

$\frac{18}{z} (\frac{1}{\sqrt{z}} \cdot \frac{\sqrt{z}}{\sqrt{z}})$

Step 7

Combine and simplify the denominator.

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

$\frac{18}{z} \cdot \frac{\sqrt{z}}{\sqrt{z} \sqrt{z}}$

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

$\frac{18}{z} \cdot \frac{\sqrt{z}}{{\sqrt{z}}^{1} \sqrt{z}}$

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

$\frac{18}{z} \cdot \frac{\sqrt{z}}{{\sqrt{z}}^{1} {\sqrt{z}}^{1}}$

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

$\frac{18}{z} \cdot \frac{\sqrt{z}}{{\sqrt{z}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{18}{z} \cdot \frac{\sqrt{z}}{{\sqrt{z}}^{2}}$

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

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

$\frac{18}{z} \cdot \frac{\sqrt{z}}{{(z^{\frac{1}{2}})}^{2}}$

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

$\frac{18}{z} \cdot \frac{\sqrt{z}}{z^{\frac{1}{2} \cdot 2}}$

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

$\frac{18}{z} \cdot \frac{\sqrt{z}}{z^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{18}{z} \cdot \frac{\sqrt{z}}{z^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{18}{z} \cdot \frac{\sqrt{z}}{z^{1}}$

Simplify.

$\frac{18}{z} \cdot \frac{\sqrt{z}}{z}$

Step 8

Multiply $\frac{18}{z} \cdot \frac{\sqrt{z}}{z}$ .

Multiply $\frac{18}{z}$ by $\frac{\sqrt{z}}{z}$ .

$\frac{18 \sqrt{z}}{z \cdot z}$

Raise $z$ to the power of $1$ .

$\frac{18 \sqrt{z}}{z^{1} z}$

Raise $z$ to the power of $1$ .

$\frac{18 \sqrt{z}}{z^{1} z^{1}}$

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

$\frac{18 \sqrt{z}}{z^{1 + 1}}$

Add $1$ and $1$ .

$\frac{18 \sqrt{z}}{z^{2}}$

Simplify square root of (18^2)/(z^3)

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