Simplify 4a^3b^2*(3a^-4b^-3)

Problem

4*a3*b2*(3*a(−4)*b(−3))

Solution

1. Group the coefficients and the variables with the same bases together.

4⋅3⋅a3⋅a(−4)⋅b2⋅b(−3)

2. Multiply the numerical coefficients to find the constant term.

4⋅3=12

3. Apply the product rule for exponents by adding the exponents of the terms with base a

a3⋅a(−4)=a(3+(−4))=a(−1)

4. Apply the product rule for exponents by adding the exponents of the terms with base b

b2⋅b(−3)=b(2+(−3))=b(−1)

5. Combine the results into a single expression.

12*a(−1)*b(−1)

6. Rewrite with positive exponents by moving the variables with negative exponents to the denominator.

12/(a*b)

Final Answer

4*a3*b2*(3*a(−4)*b(−3))=12/(a*b)

Want more problems? Check here!