Algebra Examples

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

Step 1

Move $p^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Move $q^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $- \frac{3 q^{4}}{p^{3}}$ .

${(- 1)}^{2} {(\frac{3 q^{4}}{p^{3}})}^{2}$

Step 4.2

Apply the product rule to $\frac{3 q^{4}}{p^{3}}$ .

${(- 1)}^{2} \frac{{(3 q^{4})}^{2}}{{(p^{3})}^{2}}$

Step 4.3

Apply the product rule to $3 q^{4}$ .

${(- 1)}^{2} \frac{3^{2} {(q^{4})}^{2}}{{(p^{3})}^{2}}$

Step 5

Simplify the expression.

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Step 5.1

Raise $- 1$ to the power of $2$ .

$1 \frac{3^{2} {(q^{4})}^{2}}{{(p^{3})}^{2}}$

Step 5.2

Multiply $\frac{3^{2} {(q^{4})}^{2}}{{(p^{3})}^{2}}$ by $1$ .

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

Step 6

Simplify the numerator.

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Step 6.1

Raise $3$ to the power of $2$ .

$\frac{9 {(q^{4})}^{2}}{{(p^{3})}^{2}}$

Step 6.2

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

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Step 6.2.1

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

$\frac{9 q^{4 \cdot 2}}{{(p^{3})}^{2}}$

Step 6.2.2

Multiply $4$ by $2$ .

$\frac{9 q^{8}}{{(p^{3})}^{2}}$

Step 7

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

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Step 7.1

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

$\frac{9 q^{8}}{p^{3 \cdot 2}}$

Step 7.2

Multiply $3$ by $2$ .

$\frac{9 q^{8}}{p^{6}}$