Simplify (x^2y^-1)^2

Problem

(x^2*y^(−1))^2

Solution

1. Apply the power of a power rule, which states that (a^m)^n=a^(m⋅n)

2. Distribute the exponent to each factor inside the parentheses by multiplying the exponents.

x^(2⋅2)*y^(−1⋅2)

3. Simplify the exponents by performing the multiplication.

x^4*y^(−2)

4. Apply the negative exponent rule, which states that a^(−n)=1/(a^n) to rewrite the expression with positive exponents.

(x^4)/(y^2)

Final Answer

(x^2*y^(−1))^2=(x^4)/(y^2)

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