Simplify ((4a^3b)/(a^2b^3))((3b^2)/(2a^2b^4))

Problem

((4*a3*b)/(a2*b3))*((3*b2)/(2*a2*b4))

Solution

1. Multiply the numerators and denominators together to combine the two fractions into a single expression.

(4*a3*b⋅3*b2)/(a2*b3⋅2*a2*b4)

2. Group like terms in the numerator and denominator by multiplying the coefficients and adding the exponents of variables with the same base.

(12*a3*b3)/(2*a4*b7)

3. Divide the coefficients by calculating the quotient of 12 and 2.

(6*a3*b3)/(a4*b7)

4. Apply the quotient rule for exponents, which states that (xm)/(xn)=x(m−n) to simplify the variables a and b

6*a(3−4)*b(3−7)

5. Simplify the exponents to find the final powers of each variable.

6*a(−1)*b(−4)

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

6/(a*b4)

Final Answer

((4*a3*b)/(a2*b3))*((3*b2)/(2*a2*b4))=6/(a*b4)

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