Algebra Examples

${(- 3 q^{- 1})}^{3} q^{2}$

Step 1

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

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

Step 2

Combine $- 3$ and $\frac{1}{q}$ .

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

Step 3

Move the negative in front of the fraction.

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

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 $- \frac{3}{q}$ .

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

Step 4.2

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

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

Step 5

Evaluate the exponents.

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Step 5.1

Raise $- 1$ to the power of $3$ .

$- \frac{3^{3}}{q^{3}} q^{2}$

Step 5.2

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

$- \frac{27}{q^{3}} q^{2}$

Step 6

Cancel the common factor of $q^{2}$ .

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Step 6.1

Move the leading negative in $- \frac{27}{q^{3}}$ into the numerator.

$\frac{- 27}{q^{3}} q^{2}$

Step 6.2

Factor $q^{2}$ out of $q^{3}$ .

$\frac{- 27}{q^{2} q} q^{2}$

Step 6.3

Cancel the common factor.

$\frac{- 27}{q^{2} q} q^{2}$

Step 6.4

Rewrite the expression.

$\frac{- 27}{q}$

Step 7

Move the negative in front of the fraction.

$- \frac{27}{q}$