Simplify b/( square root of 4b^5)

$\frac{b}{\sqrt{4 b^{5}}}$

Step 1

Simplify the denominator.

Rewrite $4 b^{5}$ as ${(2 b^{2})}^{2} b$ .

Rewrite $4$ as $2^{2}$ .

$\frac{b}{\sqrt{2^{2} b^{5}}}$

Factor out $b^{4}$ .

$\frac{b}{\sqrt{2^{2} (b^{4} b)}}$

Rewrite $b^{4}$ as ${(b^{2})}^{2}$ .

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

Rewrite $2^{2} {(b^{2})}^{2}$ as ${(2 b^{2})}^{2}$ .

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

Pull terms out from under the radical.

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

Step 2

Cancel the common factor of $b$ and $b^{2}$ .

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

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

Factor $b$ out of $b^{1}$ .

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

Cancel the common factors.

Factor $b$ out of $2 b^{2} \sqrt{b}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

Move $\sqrt{b}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 5

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

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

Simplify b/( square root of 4b^5)

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