Answer:
x^4/y^2.
Explanation:
The expression (x^2y^-1)^2 can be simplified by applying the exponent rules. Let's break it down step-by-step: 1. Start by expanding the exponent to each term inside the parentheses: (x^2)^2 * (y^-1)^2. 2. Simplify each term separately: - For the term (x^2)^2, we multiply the exponents, so we have x^(2*2) = x^4. - For the term (y^-1)^2, we multiply the exponents, which gives us y^(-1*2) = y^-2. 3. Rewrite the expression with the simplified terms: x^4 * y^-2. 4. Now, let's simplify the expression further. Recall that y^-2 means the reciprocal of y^2, so we can rewrite it as 1/y^2. Therefore, the expression becomes: x^4 * 1/y^2. 5. Simplify the expression by multiplying the terms together: x^4/y^2. So, the simplified form of (x^2y^-1)^2 is x^4/y^2.