Solve 1/2ab*3/2ab^2

$$\frac { 1 } { 2 } a b \times \frac { 3 } { 2 } a b ^ { 2 }$$

Evaluate

$$\frac{3a^{2}b^{3}}{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{2}\right)^{1}a^{1}b^{1}\times \left(\frac{3}{2}\right)^{1}a^{1}b^{2}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{1}{2}\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{1}a^{1}b^{1}b^{2}$$

To multiply powers of the same base, add their exponents.

$$\left(\frac{1}{2}\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{1+1}b^{1+2}$$

Add the exponents 1 and 1.

$$\left(\frac{1}{2}\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{2}b^{1+2}$$

Add the exponents 1 and 2.

$$\left(\frac{1}{2}\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{2}b^{3}$$

Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{3}{4}a^{2}b^{3}$$

Differentiate w.r.t. a

$$\frac{3ab^{3}}{2}$$