Simplify ((a^-2)^3b^4)/(b^-2)

$\frac{{(a^{- 2})}^{3} b^{4}}{b^{- 2}}$

Move $b^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(a^{- 2})}^{3} b^{4} b^{2}$

Multiply $b^{4}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

${(a^{- 2})}^{3} (b^{2} b^{4})$

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

${(a^{- 2})}^{3} b^{2 + 4}$

Add $2$ and $4$ .

${(a^{- 2})}^{3} b^{6}$

Multiply the exponents in ${(a^{- 2})}^{3}$ .

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

$a^{- 2 \cdot 3} b^{6}$

Multiply $- 2$ by $3$ .

$a^{- 6} b^{6}$

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

$\frac{1}{a^{6}} b^{6}$

Combine $\frac{1}{a^{6}}$ and $b^{6}$ .

$\frac{b^{6}}{a^{6}}$