Solve (3/2a^3b^-2)(-12a^-4b^5)

$$( \frac { 3 } { 2 } a ^ { 3 } b ^ { - 2 } ) ( - 12 a ^ { - 4 } b ^ { 5 } )$$

Evaluate

$$-\frac{18b^{3}}{a}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(\frac{3}{2}\right)^{1}a^{3}b^{-2}\left(-12\right)^{1}a^{-4}b^{5}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{3}{2}\right)^{1}\left(-12\right)^{1}a^{3}a^{-4}b^{-2}b^{5}$$

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

$$\left(\frac{3}{2}\right)^{1}\left(-12\right)^{1}a^{3-4}b^{-2+5}$$

Add the exponents 3 and -4.

$$\left(\frac{3}{2}\right)^{1}\left(-12\right)^{1}\times \frac{1}{a}b^{-2+5}$$

Add the exponents -2 and 5.

$$\left(\frac{3}{2}\right)^{1}\left(-12\right)^{1}\times \frac{1}{a}b^{3}$$

Multiply \frac{3}{2} times -12.

$$-18\times \frac{1}{a}b^{3}$$

Differentiate w.r.t. b

$$-\frac{54b^{2}}{a}$$