Simplify 3x^2(3xy^-1)^-2

Problem

3*x^2*(3*x*y^(−1))^(−2)

Solution

1. Apply the power of a product rule to the term inside the parentheses, which states (a*b*c)^n=a^n*b^n*c^n

3*x^2*(3^(−2)*x^(−2)*(y^(−1))^(−2))

2. Apply the power of a power rule to the y term, which states (a^m)^n=a^(m⋅n)

3*x^2*(3^(−2)*x^(−2)*y^2)

3. Group like bases together to prepare for simplification.

3⋅3^(−2)⋅x^2⋅x^(−2)⋅y^2

4. Apply the product rule for exponents by adding the exponents of terms with the same base, a^m*a^n=a^(m+n)

3^(1−2)*x^(2−2)*y^2

5. Simplify the exponents by performing the addition and subtraction.

3^(−1)*x^0*y^2

6. Apply the zero exponent rule x^0=1 and the negative exponent rule a^(−n)=1/(a^n)

1/3⋅1⋅y^2

7. Combine the terms into a single fraction.

(y^2)/3

Final Answer

3*x^2*(3*x*y^(−1))^(−2)=(y^2)/3

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