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

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

Evaluate

$$\frac{a^{3}b^{7}}{2}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 1 and 2.

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

Add the exponents 3 and 4.

$$\left(-\frac{3}{4}\right)^{1}\left(-\frac{2}{3}\right)^{1}a^{3}b^{7}$$

Multiply -\frac{3}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{2}a^{3}b^{7}$$

Differentiate w.r.t. a

$$\frac{3a^{2}b^{7}}{2}$$