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

Problem

3*x2*(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=an*bn*cn

3*x2*(3(−2)*x(−2)*(y(−1))(−2))

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

3*x2*(3(−2)*x(−2)*y2)

3. Group like bases together to prepare for simplification.

3⋅3(−2)⋅x2⋅x(−2)⋅y2

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

3(1−2)*x(2−2)*y2

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

3(−1)*x0*y2

6. Apply the zero exponent rule x0=1 and the negative exponent rule a(−n)=1/(an)

1/3⋅1⋅y2

7. Combine the terms into a single fraction.

(y2)/3

Final Answer

3*x2*(3*x*y(−1))(−2)=(y2)/3

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