Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(4^2m^2n/n^3)^−2
To simplify the expression, we can apply the properties of exponents. First, we can apply the power of a quotient rule to simplify the expression inside the parentheses:
(4^2m^2n/n^3)^-2 = 4^(-2)*m^(-2)*n^(-2)/n^(-6)
= (1/4^2)*(1/m^2)*(1/n^2)*(n^6)
Next, we can simplify the numerical part:
(1/4^2)*(1/m^2)*(1/n^2)*(n^6) = 1/16m^2n^2n^6
= 1/16m^2n^8
Therefore, the simplified expression is 1/16m^2n^8.