Simplify (-q^-1)^4

${(- q^{- 1})}^{4}$

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

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

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

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Apply the product rule to $- \frac{1}{q}$ .

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

Apply the product rule to $\frac{1}{q}$ .

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

Raise $- 1$ to the power of $4$ .

$1 \frac{1^{4}}{q^{4}}$

Multiply $\frac{1^{4}}{q^{4}}$ by $1$ .

$\frac{1^{4}}{q^{4}}$

One to any power is one.

$\frac{1}{q^{4}}$

Simplify (-q^-1)^4