Simplify (a^4)^-5*a^13

${(a^{4})}^{- 5} \cdot a^{13}$

Step 1

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

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

$a^{4 \cdot - 5} \cdot a^{13}$

Multiply $4$ by $- 5$ .

$a^{- 20} \cdot a^{13}$

Step 2

Multiply $a^{- 20}$ by $a^{13}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{- 20 + 13}$

Add $- 20$ and $13$ .

$a^{- 7}$

Step 3

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

$\frac{1}{a^{7}}$