Evaluate (x^-2x^-3)^4

${(x^{- 2} x^{- 3})}^{4}$

Multiply $x^{- 2}$ by $x^{- 3}$ by adding the exponents.

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

${(x^{- 2 - 3})}^{4}$

Subtract $3$ from $- 2$ .

${(x^{- 5})}^{4}$

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

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

$x^{- 5 \cdot 4}$

Multiply $- 5$ by $4$ .

$x^{- 20}$

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

$\frac{1}{x^{20}}$