Simplify (3AB)^-1(A^2B^-1)^2

Problem

(3*A*B)(−1)*(A2*B(−1))2

Solution

1. Apply the power of a product rule to the first term (3*A*B)(−1) by distributing the exponent −1 to each factor inside the parentheses.

(3*A*B)(−1)=3(−1)*A(−1)*B(−1)

2. Apply the power of a power rule to the second term (A2*B(−1))2 by multiplying the exponents.

(A2*B(−1))2=A(2⋅2)*B(−1⋅2)

(A2*B(−1))2=A4*B(−2)

3. Combine the terms by multiplying the results from the previous steps.

3(−1)*A(−1)*B(−1)*A4*B(−2)

4. Group like bases and add their exponents according to the product rule xm*xn=x(m+n)

3(−1)*A(−1+4)*B(−1−2)

3(−1)*A3*B(−3)

5. Rewrite with positive exponents by moving terms with negative exponents to the denominator.

(A3)/(3*B3)

(A3)/(3*B3)

Final Answer

(3*A*B)(−1)*(A2*B(−1))2=(A3)/(3*B3)

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