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:

`((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:

`(a^(-2*-3)*b^(2*-3))/(a^(2*-3)*b^(-10*-3))=\\(a^(6)*b^(-6))/(a^(-6)*b^(30))=`

By definition we have to:

`a^(-1)=(1)/(a^1)=(1)/(a)`

So:

`(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:

`(a^(12))/(b^(36))`

Answer:

`(a^(12))/(b^(36))`