Basic Math Examples

$(\frac{12 p^{2} q}{5 p}) (\frac{15 p^{4} q^{3}}{12 q})$

Step 1

Combine.

$\frac{12 p^{2} q (15 p^{4} q^{3})}{5 p (12 q)}$

Step 2

Multiply $p^{2}$ by $p^{4}$ by adding the exponents.

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Step 2.1

Move $p^{4}$ .

$\frac{12 (p^{4} p^{2}) q (15 q^{3})}{5 p (12 q)}$

Step 2.2

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

$\frac{12 p^{4 + 2} q (15 q^{3})}{5 p (12 q)}$

Step 2.3

Add $4$ and $2$ .

$\frac{12 p^{6} q (15 q^{3})}{5 p (12 q)}$

Step 3

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

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Step 3.1

Move $q^{3}$ .

$\frac{12 p^{6} (q^{3} q) \cdot 15}{5 p (12 q)}$

Step 3.2

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

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Step 3.2.1

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

$\frac{12 p^{6} (q^{3} q^{1}) \cdot 15}{5 p (12 q)}$

Step 3.2.2

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

$\frac{12 p^{6} q^{3 + 1} \cdot 15}{5 p (12 q)}$

Step 3.3

Add $3$ and $1$ .

$\frac{12 p^{6} q^{4} \cdot 15}{5 p (12 q)}$

Step 4

Cancel the common factor of $12$ .

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Step 4.1

Cancel the common factor.

$\frac{12 p^{6} q^{4} \cdot 15}{5 p (12 q)}$

Step 4.2

Rewrite the expression.

$\frac{p^{6} q^{4} \cdot 15}{5 p (q)}$

Step 5

Cancel the common factor of $p^{6}$ and $p$ .

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Step 5.1

Factor $p$ out of $p^{6} q^{4} \cdot 15$ .

$\frac{p (p^{5} q^{4} \cdot 15)}{5 p (q)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $p$ out of $5 p (q)$ .

$\frac{p (p^{5} q^{4} \cdot 15)}{p (5 (q))}$

Step 5.2.2

Cancel the common factor.

$\frac{p (p^{5} q^{4} \cdot 15)}{p (5 (q))}$

Step 5.2.3

Rewrite the expression.

$\frac{p^{5} q^{4} \cdot 15}{5 (q)}$

Step 6

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

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Step 6.1

Factor $q$ out of $p^{5} q^{4} \cdot 15$ .

$\frac{q (p^{5} q^{3} \cdot 15)}{5 (q)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $q$ out of $5 (q)$ .

$\frac{q (p^{5} q^{3} \cdot 15)}{q \cdot 5}$

Step 6.2.2

Cancel the common factor.

$\frac{q (p^{5} q^{3} \cdot 15)}{q \cdot 5}$

Step 6.2.3

Rewrite the expression.

$\frac{p^{5} q^{3} \cdot 15}{5}$

Step 7

Cancel the common factor of $15$ and $5$ .

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Step 7.1

Factor $5$ out of $p^{5} q^{3} \cdot 15$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $5$ out of $5$ .

$\frac{5 (p^{5} q^{3} \cdot 3)}{5 (1)}$

Step 7.2.2

Cancel the common factor.

$\frac{5 (p^{5} q^{3} \cdot 3)}{5 \cdot 1}$

Step 7.2.3

Rewrite the expression.

$\frac{p^{5} q^{3} \cdot 3}{1}$

Step 7.2.4

Divide $p^{5} q^{3} \cdot 3$ by $1$ .

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

Step 8

Move $3$ to the left of $p^{5} q^{3}$ .

$3 p^{5} q^{3}$