Basic Math Examples

${(p^{2} q^{4})}^{- 2} {(p^{4} q^{2})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(p^{2} q^{4})}^{2}} {(p^{4} q^{2})}^{2}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $p^{2} q^{4}$ .

$\frac{1}{{(p^{2})}^{2} {(q^{4})}^{2}} {(p^{4} q^{2})}^{2}$

Step 2.2

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

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Step 2.2.1

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

$\frac{1}{p^{2 \cdot 2} {(q^{4})}^{2}} {(p^{4} q^{2})}^{2}$

Step 2.2.2

Multiply $2$ by $2$ .

$\frac{1}{p^{4} {(q^{4})}^{2}} {(p^{4} q^{2})}^{2}$

Step 2.3

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

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Step 2.3.1

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

$\frac{1}{p^{4} q^{4 \cdot 2}} {(p^{4} q^{2})}^{2}$

Step 2.3.2

Multiply $4$ by $2$ .

$\frac{1}{p^{4} q^{8}} {(p^{4} q^{2})}^{2}$

Step 3

Simplify terms.

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Step 3.1

Apply the product rule to $p^{4} q^{2}$ .

$\frac{1}{p^{4} q^{8}} ({(p^{4})}^{2} {(q^{2})}^{2})$

Step 3.2

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

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Step 3.2.1

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

$\frac{1}{p^{4} q^{8}} (p^{4 \cdot 2} {(q^{2})}^{2})$

Step 3.2.2

Multiply $4$ by $2$ .

$\frac{1}{p^{4} q^{8}} (p^{8} {(q^{2})}^{2})$

Step 3.3

Cancel the common factor of $p^{4}$ .

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Step 3.3.1

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

$\frac{1}{p^{4} (q^{8})} (p^{8} {(q^{2})}^{2})$

Step 3.3.2

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

$\frac{1}{p^{4} (q^{8})} (p^{4} (p^{4} {(q^{2})}^{2}))$

Step 3.3.3

Cancel the common factor.

$\frac{1}{p^{4} q^{8}} (p^{4} (p^{4} {(q^{2})}^{2}))$

Step 3.3.4

Rewrite the expression.

$\frac{1}{q^{8}} (p^{4} {(q^{2})}^{2})$

Step 3.4

Combine $p^{4}$ and $\frac{1}{q^{8}}$ .

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

Step 3.5

Combine $\frac{p^{4}}{q^{8}}$ and ${(q^{2})}^{2}$ .

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

Step 3.6

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

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Step 3.6.1

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

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

Step 3.6.2

Multiply $2$ by $2$ .

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

Step 3.7

Cancel the common factor of $q^{4}$ and $q^{8}$ .

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Step 3.7.1

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

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

Step 3.7.2

Cancel the common factors.

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Step 3.7.2.1

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

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

Step 3.7.2.2

Cancel the common factor.

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

Step 3.7.2.3

Rewrite the expression.

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