For this case we must solve the following expression:
[tex]\frac{(a^{-2}*b^2)^{-3}}{(a^2*b^{-10})^{-3}}[/tex]
By definition of power properties we have to:
[tex](a^n)^m=a^{n*m}[/tex]
Rewriting we have to:
[tex]\frac{a^{-2*-3}*b^{2*-3}}{a^{2*-3}*b^{-10*-3}}=\\\frac{a^{6}*b^{-6}}{a^{-6}*b^{30}}=[/tex]
By definition we have to:
[tex]a^{-1}=\frac{1}{a^1}=\frac{1}{a}[/tex]
So:
[tex]\frac{a^6*a^6}{b^6*b^{30}}=[/tex]
By definition of multiplication of powers of the same base, we place the same base and add the exponents:
[tex]\frac{a^{12}}{b^{36}}[/tex]
Answer:
[tex]\frac{a^{12}}{b^{36}}[/tex]
