Divide ((6m^7)/(30n))÷((12m^3n)/25)

$\frac{6 m^{7}}{30 n} \div \frac{12 m^{3} n}{25}$

To divide by a fraction, multiply by its reciprocal.

$\frac{6 m^{7}}{30 n} \cdot \frac{25}{12 m^{3} n}$

Cancel the common factor of $6 m^{3}$ .

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Factor $6 m^{3}$ out of $6 m^{7}$ .

$\frac{6 m^{3} (m^{4})}{30 n} \cdot \frac{25}{12 m^{3} n}$

Factor $6 m^{3}$ out of $12 m^{3} n$ .

$\frac{6 m^{3} (m^{4})}{30 n} \cdot \frac{25}{6 m^{3} (2 n)}$

Cancel the common factor.

$\frac{6 m^{3} m^{4}}{30 n} \cdot \frac{25}{6 m^{3} (2 n)}$

Rewrite the expression.

$\frac{m^{4}}{30 n} \cdot \frac{25}{2 n}$

Cancel the common factor of $5$ .

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Factor $5$ out of $30 n$ .

$\frac{m^{4}}{5 (6 n)} \cdot \frac{25}{2 n}$

Factor $5$ out of $25$ .

$\frac{m^{4}}{5 (6 n)} \cdot \frac{5 (5)}{2 n}$

Cancel the common factor.

$\frac{m^{4}}{5 (6 n)} \cdot \frac{5 \cdot 5}{2 n}$

Rewrite the expression.

$\frac{m^{4}}{6 n} \cdot \frac{5}{2 n}$

Multiply $\frac{m^{4}}{6 n}$ and $\frac{5}{2 n}$ .

$\frac{m^{4} \cdot 5}{6 n (2 n)}$

Multiply $2$ by $6$ .

$\frac{m^{4} \cdot 5}{12 n \cdot n}$

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

$\frac{m^{4} \cdot 5}{12 (n^{1} n)}$

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

$\frac{m^{4} \cdot 5}{12 (n^{1} n^{1})}$

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

$\frac{m^{4} \cdot 5}{12 n^{1 + 1}}$

Add $1$ and $1$ .

$\frac{m^{4} \cdot 5}{12 n^{2}}$

Move $5$ to the left of $m^{4}$ .

$\frac{5 m^{4}}{12 n^{2}}$

Divide ((6m^7)/(30n))÷((12m^3n)/25)

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