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

Question

asked Jun 21, 2020 161k views

2 Answers

Jim Blake · Answer 1 · 2020-06-27T02:16:14+0000

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: