Solve (-4r^-2s^-8)(9r^4s^3)

$$( - 4 r ^ { - 2 } s ^ { - 8 } ) ( 9 r ^ { 4 } s ^ { 3 } )$$

Evaluate

$$-\frac{36r^{2}}{s^{5}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-4\right)^{1}r^{-2}s^{-8}\times 9^{1}r^{4}s^{3}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{1}\times 9^{1}r^{-2}r^{4}s^{-8}s^{3}$$

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

$$\left(-4\right)^{1}\times 9^{1}r^{-2+4}s^{-8+3}$$

Add the exponents -2 and 4.

$$\left(-4\right)^{1}\times 9^{1}r^{2}s^{-8+3}$$

Add the exponents -8 and 3.

$$\left(-4\right)^{1}\times 9^{1}r^{2}s^{-5}$$

Multiply -4 times 9.

$$-36r^{2}\times \frac{1}{s^{5}}$$

Differentiate w.r.t. s

$$\frac{180r^{2}}{s^{6}}$$