Simplify (6b^3)/( square root of 4b^9)

$\frac{6 b^{3}}{\sqrt{4 b^{9}}}$

Simplify the denominator.

Rewrite $4 b^{9}$ as ${(2 b^{4})}^{2} b$ .

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

$\frac{6 b^{3}}{\sqrt{2^{2} b^{9}}}$

Factor out $b^{8}$ .

$\frac{6 b^{3}}{\sqrt{2^{2} (b^{8} b)}}$

Rewrite $b^{8}$ as ${(b^{4})}^{2}$ .

$\frac{6 b^{3}}{\sqrt{2^{2} ({(b^{4})}^{2} b)}}$

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

$\frac{6 b^{3}}{\sqrt{{(2 b^{4})}^{2} b}}$

Pull terms out from under the radical.

$\frac{6 b^{3}}{2 b^{4} \sqrt{b}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 b^{3}$ .

$\frac{2 (3 b^{3})}{2 b^{4} \sqrt{b}}$

Cancel the common factors.

Factor $2$ out of $2 b^{4} \sqrt{b}$ .

$\frac{2 (3 b^{3})}{2 (b^{4} \sqrt{b})}$

Cancel the common factor.

$\frac{2 (3 b^{3})}{2 (b^{4} \sqrt{b})}$

Rewrite the expression.

$\frac{3 b^{3}}{b^{4} \sqrt{b}}$

Cancel the common factor of $b^{3}$ and $b^{4}$ .

Factor $b^{3}$ out of $3 b^{3}$ .

$\frac{b^{3} \cdot 3}{b^{4} \sqrt{b}}$

Cancel the common factors.

Factor $b^{3}$ out of $b^{4} \sqrt{b}$ .

$\frac{b^{3} \cdot 3}{b^{3} (b \sqrt{b})}$

Cancel the common factor.

$\frac{b^{3} \cdot 3}{b^{3} (b \sqrt{b})}$

Rewrite the expression.

$\frac{3}{b \sqrt{b}}$

Multiply $\frac{3}{b \sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

$\frac{3}{b \sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}}$

Combine and simplify the denominator.

Multiply $\frac{3}{b \sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

$\frac{3 \sqrt{b}}{b \sqrt{b} \sqrt{b}}$

Move $\sqrt{b}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{3 \sqrt{b}}{b \cdot b}$

Multiply $b$ by $b$ .

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

Simplify (6b^3)/( square root of 4b^9)

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