Fully simplify the following: (2x^2/2x^3y^2*x^2)^4
Start by simplifying the expression inside the parentheses:
2x^2 / 2x^3y^2 * x^2 = (2/2) * (x^2/x^3) * (1/y^2) * x^2
= 1 * (1/x) * (1/y^2) * x^2
= x / y^2
Then raise this simplified expression to the 4th power:
(x / y^2)^4 = x^4 / y^8
Therefore, the fully simplified expression is x^4 / y^8.