Simplify (a^-5c^-9)^-4

${(a^{- 5} c^{- 9})}^{- 4}$

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

${(\frac{1}{a^{5}} c^{- 9})}^{- 4}$

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

${(\frac{1}{a^{5}} \cdot \frac{1}{c^{9}})}^{- 4}$

Multiply $\frac{1}{a^{5}}$ and $\frac{1}{c^{9}}$ .

${(\frac{1}{a^{5} c^{9}})}^{- 4}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(a^{5} c^{9})}^{4}$

Apply the product rule to $a^{5} c^{9}$ .

${(a^{5})}^{4} {(c^{9})}^{4}$

Multiply the exponents in ${(a^{5})}^{4}$ .

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

$a^{5 \cdot 4} {(c^{9})}^{4}$

Multiply $5$ by $4$ .

$a^{20} {(c^{9})}^{4}$

Multiply the exponents in ${(c^{9})}^{4}$ .

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

$a^{20} c^{9 \cdot 4}$

Multiply $9$ by $4$ .

$a^{20} c^{36}$

Simplify (a^-5c^-9)^-4

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