Question

Simplify (a^-2b^2)^-3/(a^2b^-10)^-3

Answer 1

The simplified expression is a^12 / 8b^33

Answer 2

For this case we must solve the following expression:

$\frac{(a^{-2}*b^2)^{-3}}{(a^2*b^{-10})^{-3}}$

By definition of power properties we have to:

$(a^n)^m=a^{n*m}$

Rewriting we have to:

$\frac{a^{-2*-3}*b^{2*-3}}{a^{2*-3}*b^{-10*-3}}=\\\frac{a^{6}*b^{-6}}{a^{-6}*b^{30}}=$

By definition we have to:

$a^{-1}=\frac{1}{a^1}=\frac{1}{a}$

So:

$\frac{a^6*a^6}{b^6*b^{30}}=$

By definition of multiplication of powers of the same base, we place the same base and add the exponents:

$\frac{a^{12}}{b^{36}}$

Answer:

$\frac{a^{12}}{b^{36}}$