Divide ((5m^2)/(7n^3))÷((10m^4)/(14an^4))

$\frac{5 m^{2}}{7 n^{3}} \div \frac{10 m^{4}}{14 a n^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 m^{2}}{7 n^{3}} \cdot \frac{14 a n^{4}}{10 m^{4}}$

Step 2

Combine.

$\frac{5 m^{2} (14 a n^{4})}{7 n^{3} (10 m^{4})}$

Step 3

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

Factor $5$ out of $5 m^{2} (14 a n^{4})$ .

$\frac{5 (m^{2} (14 a n^{4}))}{7 n^{3} (10 m^{4})}$

Cancel the common factors.

Factor $5$ out of $7 n^{3} (10 m^{4})$ .

$\frac{5 (m^{2} (14 a n^{4}))}{5 (7 n^{3} (2 m^{4}))}$

Cancel the common factor.

$\frac{5 (m^{2} (14 a n^{4}))}{5 (7 n^{3} (2 m^{4}))}$

Rewrite the expression.

$\frac{m^{2} (14 a n^{4})}{7 n^{3} (2 m^{4})}$

Step 4

Cancel the common factors.

Factor $m^{2}$ out of $7 n^{3} (2 m^{4})$ .

$\frac{m^{2} (14 a n^{4})}{m^{2} (7 n^{3} (2 m^{2}))}$

Cancel the common factor.

$\frac{m^{2} (14 a n^{4})}{m^{2} (7 n^{3} (2 m^{2}))}$

Rewrite the expression.

$\frac{14 a n^{4}}{7 n^{3} (2 m^{2})}$

Step 5

Cancel the common factor of $14$ and $7$ .

Factor $7$ out of $14 a n^{4}$ .

$\frac{7 (2 a n^{4})}{7 n^{3} (2 m^{2})}$

Cancel the common factors.

Factor $7$ out of $7 n^{3} (2 m^{2})$ .

$\frac{7 (2 a n^{4})}{7 (n^{3} (2 m^{2}))}$

Cancel the common factor.

$\frac{7 (2 a n^{4})}{7 (n^{3} (2 m^{2}))}$

Rewrite the expression.

$\frac{2 a n^{4}}{n^{3} (2 m^{2})}$

Step 6

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a n^{4}}{n^{3} (2 m^{2})}$

Rewrite the expression.

$\frac{a n^{4}}{n^{3} (m^{2})}$

Step 7

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

Factor $n^{3}$ out of $a n^{4}$ .

$\frac{n^{3} (a n)}{n^{3} (m^{2})}$

Cancel the common factors.

Cancel the common factor.

$\frac{n^{3} (a n)}{n^{3} m^{2}}$

Rewrite the expression.

$\frac{a n}{m^{2}}$

Divide ((5m^2)/(7n^3))÷((10m^4)/(14an^4))

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