Simplify (ab^2)^-4

${(a b^{2})}^{- 4}$

Step 1

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

$\frac{1}{{(a b^{2})}^{4}}$

Step 2

Simplify the denominator.

Apply the product rule to $a b^{2}$ .

$\frac{1}{a^{4} {(b^{2})}^{4}}$

Multiply the exponents in ${(b^{2})}^{4}$ .

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

$\frac{1}{a^{4} b^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{1}{a^{4} b^{8}}$