simplify ((mn^3)^2)*(((2^-2)(m^-1)(n^3))^-2)

Answer 1

First, we need to simplify each term separately before evaluating the powers.

Starting with the first term, (mn^3)^2:
(mn^3)^2 = m^2 * (n^3)^2
= m^2 * n^6

Next, moving on to the second term, (((2^-2)(m^-1)(n^3))^-2):
(((2^-2)(m^-1)(n^3))^-2) = (2^-2)^-2 * (m^-1)^-2 * (n^3)^-2
= (2^4) * (m^2) * (n^-6)
= (16m^2)/n^6

Now, combining the simplified terms and evaluating the powers:
((mn^3)^2)*(((2^-2)(m^-1)(n^3))^-2) = (m^2 * n^6) * ((16m^2)/n^6)
= (m^2 * n^6) * (16m^2) / (n^6)
= 16m^4

Therefore, the simplified expression is 16m^4.