Divide ((14p^2q^3)/(2pq))÷((7p^2q^2)/(6p^3q^2))

$\frac{14 p^{2} q^{3}}{2 p q} \div \frac{7 p^{2} q^{2}}{6 p^{3} q^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{14 p^{2} q^{3}}{2 p q} \cdot \frac{6 p^{3} q^{2}}{7 p^{2} q^{2}}$

Step 2

Combine.

$\frac{14 p^{2} q^{3} (6 p^{3} q^{2})}{2 p q (7 p^{2} q^{2})}$

Step 3

Multiply $p^{2}$ by $p^{3}$ by adding the exponents.

Move $p^{3}$ .

$\frac{14 (p^{3} p^{2}) q^{3} (6 q^{2})}{2 p q (7 p^{2} q^{2})}$

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

$\frac{14 p^{3 + 2} q^{3} (6 q^{2})}{2 p q (7 p^{2} q^{2})}$

Add $3$ and $2$ .

$\frac{14 p^{5} q^{3} (6 q^{2})}{2 p q (7 p^{2} q^{2})}$

Step 4

Multiply $q^{3}$ by $q^{2}$ by adding the exponents.

Move $q^{2}$ .

$\frac{14 p^{5} (q^{2} q^{3}) \cdot 6}{2 p q (7 p^{2} q^{2})}$

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

$\frac{14 p^{5} q^{2 + 3} \cdot 6}{2 p q (7 p^{2} q^{2})}$

Add $2$ and $3$ .

$\frac{14 p^{5} q^{5} \cdot 6}{2 p q (7 p^{2} q^{2})}$

Step 5

Multiply $p$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$\frac{14 p^{5} q^{5} \cdot 6}{2 (p^{2} p) q (7 q^{2})}$

Multiply $p^{2}$ by $p$ .

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

$\frac{14 p^{5} q^{5} \cdot 6}{2 (p^{2} p^{1}) q (7 q^{2})}$

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

$\frac{14 p^{5} q^{5} \cdot 6}{2 p^{2 + 1} q (7 q^{2})}$

Add $2$ and $1$ .

$\frac{14 p^{5} q^{5} \cdot 6}{2 p^{3} q (7 q^{2})}$

Step 6

Multiply $q$ by $q^{2}$ by adding the exponents.

Move $q^{2}$ .

$\frac{14 p^{5} q^{5} \cdot 6}{2 p^{3} (q^{2} q) \cdot 7}$

Multiply $q^{2}$ by $q$ .

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

$\frac{14 p^{5} q^{5} \cdot 6}{2 p^{3} (q^{2} q^{1}) \cdot 7}$

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

$\frac{14 p^{5} q^{5} \cdot 6}{2 p^{3} q^{2 + 1} \cdot 7}$

Add $2$ and $1$ .

$\frac{14 p^{5} q^{5} \cdot 6}{2 p^{3} q^{3} \cdot 7}$

Step 7

Cancel the common factor of $14$ and $2$ .

Factor $2$ out of $14 p^{5} q^{5} \cdot 6$ .

$\frac{2 (7 p^{5} q^{5} \cdot 6)}{2 p^{3} q^{3} \cdot 7}$

Cancel the common factors.

Factor $2$ out of $2 p^{3} q^{3} \cdot 7$ .

$\frac{2 (7 p^{5} q^{5} \cdot 6)}{2 (p^{3} q^{3} \cdot 7)}$

Cancel the common factor.

$\frac{2 (7 p^{5} q^{5} \cdot 6)}{2 (p^{3} q^{3} \cdot 7)}$

Rewrite the expression.

$\frac{7 p^{5} q^{5} \cdot 6}{p^{3} q^{3} \cdot 7}$

Step 8

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 p^{5} q^{5} \cdot 6}{p^{3} q^{3} \cdot 7}$

Rewrite the expression.

$\frac{p^{5} q^{5} \cdot 6}{p^{3} q^{3}}$

Step 9

Cancel the common factor of $p^{5}$ and $p^{3}$ .

Factor $p^{3}$ out of $p^{5} q^{5} \cdot 6$ .

$\frac{p^{3} (p^{2} q^{5} \cdot 6)}{p^{3} q^{3}}$

Cancel the common factors.

Factor $p^{3}$ out of $p^{3} q^{3}$ .

$\frac{p^{3} (p^{2} q^{5} \cdot 6)}{p^{3} (q^{3})}$

Cancel the common factor.

$\frac{p^{3} (p^{2} q^{5} \cdot 6)}{p^{3} q^{3}}$

Rewrite the expression.

$\frac{p^{2} q^{5} \cdot 6}{q^{3}}$

Step 10

Cancel the common factor of $q^{5}$ and $q^{3}$ .

Factor $q^{3}$ out of $p^{2} q^{5} \cdot 6$ .

$\frac{q^{3} (p^{2} q^{2} \cdot 6)}{q^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{q^{3} (p^{2} q^{2} \cdot 6)}{q^{3} \cdot 1}$

Cancel the common factor.

$\frac{q^{3} (p^{2} q^{2} \cdot 6)}{q^{3} \cdot 1}$

Rewrite the expression.

$\frac{p^{2} q^{2} \cdot 6}{1}$

Divide $p^{2} q^{2} \cdot 6$ by $1$ .

$p^{2} q^{2} \cdot 6$

Step 11

Move $6$ to the left of $p^{2} q^{2}$ .

$6 p^{2} q^{2}$

Divide ((14p^2q^3)/(2pq))÷((7p^2q^2)/(6p^3q^2))

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