Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $p^{2} q$ .

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

Step 1.2

Multiply the exponents in ${(p^{2})}^{4}$ .

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Step 1.2.1

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

$\frac{p^{2 \cdot 4} q^{4}}{{(p q^{3})}^{2}}$

Step 1.2.2

Multiply $2$ by $4$ .

$\frac{p^{8} q^{4}}{{(p q^{3})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $p q^{3}$ .

$\frac{p^{8} q^{4}}{p^{2} {(q^{3})}^{2}}$

Step 2.2

Multiply the exponents in ${(q^{3})}^{2}$ .

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Step 2.2.1

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

$\frac{p^{8} q^{4}}{p^{2} q^{3 \cdot 2}}$

Step 2.2.2

Multiply $3$ by $2$ .

$\frac{p^{8} q^{4}}{p^{2} q^{6}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $p^{8}$ and $p^{2}$ .

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Step 3.1.1

Factor $p^{2}$ out of $p^{8} q^{4}$ .

$\frac{p^{2} (p^{6} q^{4})}{p^{2} q^{6}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $p^{2}$ out of $p^{2} q^{6}$ .

$\frac{p^{2} (p^{6} q^{4})}{p^{2} (q^{6})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{p^{2} (p^{6} q^{4})}{p^{2} q^{6}}$

Step 3.1.2.3

Rewrite the expression.

$\frac{p^{6} q^{4}}{q^{6}}$

Step 3.2

Cancel the common factor of $q^{4}$ and $q^{6}$ .

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Step 3.2.1

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

$\frac{q^{4} p^{6}}{q^{6}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $q^{4}$ out of $q^{6}$ .

$\frac{q^{4} p^{6}}{q^{4} q^{2}}$

Step 3.2.2.2

Cancel the common factor.

$\frac{q^{4} p^{6}}{q^{4} q^{2}}$

Step 3.2.2.3

Rewrite the expression.

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