Simplify 5/( square root of 4m^7)

$\frac{5}{\sqrt{4 m^{7}}}$

Simplify the denominator.

Rewrite $4 m^{7}$ as ${(2 m^{3})}^{2} m$ .

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

$\frac{5}{\sqrt{2^{2} m^{7}}}$

Factor out $m^{6}$ .

$\frac{5}{\sqrt{2^{2} (m^{6} m)}}$

Rewrite $m^{6}$ as ${(m^{3})}^{2}$ .

$\frac{5}{\sqrt{2^{2} ({(m^{3})}^{2} m)}}$

Rewrite $2^{2} {(m^{3})}^{2}$ as ${(2 m^{3})}^{2}$ .

$\frac{5}{\sqrt{{(2 m^{3})}^{2} m}}$

Pull terms out from under the radical.

$\frac{5}{2 m^{3} \sqrt{m}}$

Multiply $\frac{5}{2 m^{3} \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

$\frac{5}{2 m^{3} \sqrt{m}} \cdot \frac{\sqrt{m}}{\sqrt{m}}$

Combine and simplify the denominator.

Multiply $\frac{5}{2 m^{3} \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

$\frac{5 \sqrt{m}}{2 m^{3} \sqrt{m} \sqrt{m}}$

Move $\sqrt{m}$ .

$\frac{5 \sqrt{m}}{2 m^{3} (\sqrt{m} \sqrt{m})}$

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

$\frac{5 \sqrt{m}}{2 m^{3} ({\sqrt{m}}^{1} \sqrt{m})}$

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

$\frac{5 \sqrt{m}}{2 m^{3} ({\sqrt{m}}^{1} {\sqrt{m}}^{1})}$

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

$\frac{5 \sqrt{m}}{2 m^{3} {\sqrt{m}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \sqrt{m}}{2 m^{3} {\sqrt{m}}^{2}}$

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

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

$\frac{5 \sqrt{m}}{2 m^{3} {(m^{\frac{1}{2}})}^{2}}$

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

$\frac{5 \sqrt{m}}{2 m^{3} m^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 \sqrt{m}}{2 m^{3} m^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \sqrt{m}}{2 m^{3} m^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 \sqrt{m}}{2 m^{3} m^{1}}$

Simplify.

$\frac{5 \sqrt{m}}{2 m^{3} m}$

Multiply $m^{3}$ by $m$ by adding the exponents.

Move $m$ .

$\frac{5 \sqrt{m}}{2 (m \cdot m^{3})}$

Multiply $m$ by $m^{3}$ .

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

$\frac{5 \sqrt{m}}{2 (m^{1} m^{3})}$

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

$\frac{5 \sqrt{m}}{2 m^{1 + 3}}$

Add $1$ and $3$ .

$\frac{5 \sqrt{m}}{2 m^{4}}$

Simplify 5/( square root of 4m^7)

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