Solve -12r^5s^4(-4rs^5)

$$- 12 r ^ { 5 } s ^ { 4 } ( - 4 r s ^ { 5 } )$$

Evaluate

$$48r^{6}s^{9}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-12\right)^{1}r^{5}s^{4}\left(-4\right)^{1}r^{1}s^{5}$$

Use the Commutative Property of Multiplication.

$$\left(-12\right)^{1}\left(-4\right)^{1}r^{5}r^{1}s^{4}s^{5}$$

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

$$\left(-12\right)^{1}\left(-4\right)^{1}r^{5+1}s^{4+5}$$

Add the exponents 5 and 1.

$$\left(-12\right)^{1}\left(-4\right)^{1}r^{6}s^{4+5}$$

Add the exponents 4 and 5.

$$\left(-12\right)^{1}\left(-4\right)^{1}r^{6}s^{9}$$

Multiply -12 times -4.

$$48r^{6}s^{9}$$

Differentiate w.r.t. r

$$288r^{5}s^{9}$$