Simplify the Radical Expression 1/( square root of 2b^3)

$\frac{1}{\sqrt{2 b^{3}}}$

Step 1

Simplify the denominator.

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

Factor out $b^{2}$ .

$\frac{1}{\sqrt{2 (b^{2} b)}}$

Reorder $2$ and $b^{2}$ .

$\frac{1}{\sqrt{b^{2} \cdot 2 b}}$

Add parentheses.

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

Pull terms out from under the radical.

$\frac{1}{| b | \sqrt{2 b}}$

Step 2

Multiply $\frac{1}{| b | \sqrt{2 b}}$ by $\frac{\sqrt{2 b}}{\sqrt{2 b}}$ .

$\frac{1}{| b | \sqrt{2 b}} \cdot \frac{\sqrt{2 b}}{\sqrt{2 b}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{1}{| b | \sqrt{2 b}}$ by $\frac{\sqrt{2 b}}{\sqrt{2 b}}$ .

$\frac{\sqrt{2 b}}{| b | \sqrt{2 b} \sqrt{2 b}}$

Move $\sqrt{2 b}$ .

$\frac{\sqrt{2 b}}{| b | (\sqrt{2 b} \sqrt{2 b})}$

Raise $\sqrt{2 b}$ to the power of $1$ .

$\frac{\sqrt{2 b}}{| b | ({\sqrt{2 b}}^{1} \sqrt{2 b})}$

Raise $\sqrt{2 b}$ to the power of $1$ .

$\frac{\sqrt{2 b}}{| b | ({\sqrt{2 b}}^{1} {\sqrt{2 b}}^{1})}$

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

$\frac{\sqrt{2 b}}{| b | {\sqrt{2 b}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{2 b}}{| b | {\sqrt{2 b}}^{2}}$

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

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

$\frac{\sqrt{2 b}}{| b | {({(2 b)}^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{1}}$

Simplify.

$\frac{\sqrt{2 b}}{| b | (2 b)}$

Step 4

Simplify the denominator.

Rewrite.

$\frac{\sqrt{2 b}}{| b | \sqrt{2 b} \sqrt{2 b}}$

Move $\sqrt{2 b}$ .

$\frac{\sqrt{2 b}}{| b | (\sqrt{2 b} \sqrt{2 b})}$

Raise $\sqrt{2 b}$ to the power of $1$ .

$\frac{\sqrt{2 b}}{| b | ({\sqrt{2 b}}^{1} \sqrt{2 b})}$

Raise $\sqrt{2 b}$ to the power of $1$ .

$\frac{\sqrt{2 b}}{| b | ({\sqrt{2 b}}^{1} {\sqrt{2 b}}^{1})}$

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

$\frac{\sqrt{2 b}}{| b | {\sqrt{2 b}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{2 b}}{| b | {\sqrt{2 b}}^{2}}$

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

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

$\frac{\sqrt{2 b}}{| b | {({(2 b)}^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{2 b}}{| b | {(2 b)}^{1}}$

Simplify.

$\frac{\sqrt{2 b}}{| b | (2 b)}$

Remove unnecessary parentheses.

$\frac{\sqrt{2 b}}{| b | \cdot 2 b}$

Step 5

Move $2$ to the left of $| b |$ .

$\frac{\sqrt{2 b}}{2 \cdot | b | b}$

Step 6

Reorder factors in $\frac{\sqrt{2 b}}{2 | b | b}$ .

$\frac{\sqrt{2 b}}{2 b | b |}$

Simplify the Radical Expression 1/( square root of 2b^3)

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