Simplify 1/( square root of 27z)

$\frac{1}{\sqrt{27 z}}$

Step 1

Simplify the denominator.

Rewrite $27 z$ as $3^{2} \cdot (3 z)$ .

Factor $9$ out of $27$ .

$\frac{1}{\sqrt{9 (3) z}}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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

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

Move $\sqrt{3 z}$ .

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

Raise $\sqrt{3 z}$ to the power of $1$ .

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

Raise $\sqrt{3 z}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{3 z}}^{2}$ as $3 z$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 z}$ as ${(3 z)}^{\frac{1}{2}}$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 4

Multiply $3$ by $3$ .

$\frac{\sqrt{3 z}}{9 z}$

Simplify 1/( square root of 27z)

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