Answer: The correct option is (C) \(x^4y^2.\)
Step-by-step explanation: We are given to select the correct expression that is equivalent to the expression below:
\(E=(x^2y)^2.\)
We will be using the following properties of exponents:
\((i)~(a^b)^c=a^{b\times c},\\\\(ii)~(ab)^c=a^cb^c.\)
We have
\(E=(x^2y)^2=(x^2)^2y^2=x^{2\times 2}y^2=x^4y^2.\)
Therefore, the required equivalent expression is \(x^4y^2.\)
Thus, (C) is the correct option.
