Solve (-6a^2b)*(-5/2ab^2)

$$( - 6 a ^ { 2 } b ) \cdot ( - \frac { 5 } { 2 } a b ^ { 2 } )$$

Evaluate

$$15\left(ab\right)^{3}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-6\right)^{1}a^{2}b^{1}\left(-\frac{5}{2}\right)^{1}a^{1}b^{2}$$

Use the Commutative Property of Multiplication.

$$\left(-6\right)^{1}\left(-\frac{5}{2}\right)^{1}a^{2}a^{1}b^{1}b^{2}$$

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

$$\left(-6\right)^{1}\left(-\frac{5}{2}\right)^{1}a^{2+1}b^{1+2}$$

Add the exponents 2 and 1.

$$\left(-6\right)^{1}\left(-\frac{5}{2}\right)^{1}a^{3}b^{1+2}$$

Add the exponents 1 and 2.

$$\left(-6\right)^{1}\left(-\frac{5}{2}\right)^{1}a^{3}b^{3}$$

Multiply -6 times -\frac{5}{2}.

$$15a^{3}b^{3}$$

Differentiate w.r.t. a

$$45a^{2}b^{3}$$