Fully simplify using exponent rules:
(2x^2/2x^3y^2×x^2)^4
(2x^2 / 2x^3y^2 * x^2)^4
= (x^2 / x^3y^2)^4 (simplifying 2/2 = 1 and canceling out x^2)
= (1/x^(3-2)y^2)^4 (simplifying x^2/x^3 = 1/x^(3-2))
= (1/x^y^2)^4
= 1^4 / x^4y^8 (simplifying 1/x = x^-1)
= 1 / x^4y^8
Are you sure
My apologies for the mistake. Let's correct it:
(2x^2 / 2x^3y^2 * x^2)^4
= (x^2 / x^3y^2 * x^2)^4
= (x^(2 - 3 - 2)y^(-2))^4
= (x^-3y^-2)^4
= x^(-3*4)y^(-2*4)
= x^-12y^-8
= 1 / (x^12y^8)
Therefore, the fully simplified expression is 1 / (x^12y^8)