Simplify (5m^3)/( square root of 10m)

$\frac{5 m^{3}}{\sqrt{10 m}}$

Step 1

Multiply $\frac{5 m^{3}}{\sqrt{10 m}}$ by $\frac{\sqrt{10 m}}{\sqrt{10 m}}$ .

$\frac{5 m^{3}}{\sqrt{10 m}} \cdot \frac{\sqrt{10 m}}{\sqrt{10 m}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{5 m^{3}}{\sqrt{10 m}}$ by $\frac{\sqrt{10 m}}{\sqrt{10 m}}$ .

$\frac{5 m^{3} \sqrt{10 m}}{\sqrt{10 m} \sqrt{10 m}}$

Raise $\sqrt{10 m}$ to the power of $1$ .

$\frac{5 m^{3} \sqrt{10 m}}{{\sqrt{10 m}}^{1} \sqrt{10 m}}$

Raise $\sqrt{10 m}$ to the power of $1$ .

$\frac{5 m^{3} \sqrt{10 m}}{{\sqrt{10 m}}^{1} {\sqrt{10 m}}^{1}}$

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

$\frac{5 m^{3} \sqrt{10 m}}{{\sqrt{10 m}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 m^{3} \sqrt{10 m}}{{\sqrt{10 m}}^{2}}$

Rewrite ${\sqrt{10 m}}^{2}$ as $10 m$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 m}$ as ${(10 m)}^{\frac{1}{2}}$ .

$\frac{5 m^{3} \sqrt{10 m}}{{({(10 m)}^{\frac{1}{2}})}^{2}}$

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

$\frac{5 m^{3} \sqrt{10 m}}{{(10 m)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 m^{3} \sqrt{10 m}}{{(10 m)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 m^{3} \sqrt{10 m}}{{(10 m)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 m^{3} \sqrt{10 m}}{{(10 m)}^{1}}$

Simplify.

$\frac{5 m^{3} \sqrt{10 m}}{10 m}$

Step 3

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $5 m^{3} \sqrt{10 m}$ .

$\frac{5 (m^{3} \sqrt{10 m})}{10 m}$

Cancel the common factors.

Factor $5$ out of $10 m$ .

$\frac{5 (m^{3} \sqrt{10 m})}{5 (2 m)}$

Cancel the common factor.

$\frac{5 (m^{3} \sqrt{10 m})}{5 (2 m)}$

Rewrite the expression.

$\frac{m^{3} \sqrt{10 m}}{2 m}$

Step 4

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

Factor $m$ out of $m^{3} \sqrt{10 m}$ .

$\frac{m (m^{2} \sqrt{10 m})}{2 m}$

Cancel the common factors.

Factor $m$ out of $2 m$ .

$\frac{m (m^{2} \sqrt{10 m})}{m \cdot 2}$

Cancel the common factor.

$\frac{m (m^{2} \sqrt{10 m})}{m \cdot 2}$

Rewrite the expression.

$\frac{m^{2} \sqrt{10 m}}{2}$

Simplify (5m^3)/( square root of 10m)

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