Use laws of exponents to simplify inside the parentheses of the given expression.
(a^-2b^2/a^2b^-1)^-3
To simplify the expression (a^-2b^2/a^2b^-1)^-3, we can apply the laws of exponents.
First, let's simplify inside the parentheses:
(a^-2b^2/a^2b^-1) can be rewritten as (a^-2/a^2) * (b^2/b^-1)
Using the law of exponents, a^m/a^n = a^(m-n):
(a^-2/a^2) * (b^2/b^-1) = a^(-2-2) * b^(2-(-1))
Now, let's simplify the exponents:
a^(-2-2) = a^(-4)
b^(2-(-1)) = b^(2+1) = b^3
Putting it all together, the expression simplifies to:
(a^-2b^2/a^2b^-1)^-3 = (a^(-4) * b^3)^-3
Now, using the law of exponents (a^m)^n = a^(m*n):
(a^(-4) * b^3)^-3 = a^(-4 * -3) * b^(3 * -3)
Simplifying further:
a^(-4 * -3) = a^12
b^(3 * -3) = b^-9
Therefore, the final simplified expression is:
(a^-2b^2/a^2b^-1)^-3 = a^12/b^9