Solve (-10/3a^2b^2)(6/5a^3b^2)

$$( \frac { - 10 } { 3 } a ^ { 2 } b ^ { 2 } ) ( \frac { 6 } { 5 } a ^ { 3 } b ^ { 2 } )$$

Evaluate

$$-4b^{4}a^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-\frac{10}{3}\right)^{1}a^{2}b^{2}\times \left(\frac{6}{5}\right)^{1}a^{3}b^{2}$$

Use the Commutative Property of Multiplication.

$$\left(-\frac{10}{3}\right)^{1}\times \left(\frac{6}{5}\right)^{1}a^{2}a^{3}b^{2}b^{2}$$

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

$$\left(-\frac{10}{3}\right)^{1}\times \left(\frac{6}{5}\right)^{1}a^{2+3}b^{2+2}$$

Add the exponents 2 and 3.

$$\left(-\frac{10}{3}\right)^{1}\times \left(\frac{6}{5}\right)^{1}a^{5}b^{2+2}$$

Add the exponents 2 and 2.

$$\left(-\frac{10}{3}\right)^{1}\times \left(\frac{6}{5}\right)^{1}a^{5}b^{4}$$

Multiply -\frac{10}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-4a^{5}b^{4}$$

Differentiate w.r.t. a

$$-20\left(ab\right)^{4}$$