Solve (-4a^2b^3)(3/2a^3b^-2)

$$( - 4 a ^ { 2 } b ^ { 3 } ) ( \frac { 3 } { 2 } a ^ { 3 } b ^ { - 2 } )$$

Evaluate

$$-6ba^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-4\right)^{1}a^{2}b^{3}\times \left(\frac{3}{2}\right)^{1}a^{3}b^{-2}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{2}a^{3}b^{3}b^{-2}$$

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

$$\left(-4\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{2+3}b^{3-2}$$

Add the exponents 2 and 3.

$$\left(-4\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{5}b^{3-2}$$

Add the exponents 3 and -2.

$$\left(-4\right)^{1}\times \left(\frac{3}{2}\right)^{1}a^{5}b^{1}$$

Multiply -4 times \frac{3}{2}.

$$-6a^{5}b$$

Differentiate w.r.t. a

$$-30ba^{4}$$