Solve (1/4r^-3s)(10r^-2s)

$$( \frac { 1 } { 4 } r ^ { - 3 } s ) ( 10 r ^ { - 2 } s )$$

Evaluate

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

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{4}\right)^{1}r^{-3}s^{1}\times 10^{1}r^{-2}s^{1}$$

Use the Commutative Property of Multiplication.

$$\left(\frac{1}{4}\right)^{1}\times 10^{1}r^{-3}r^{-2}s^{1}s^{1}$$

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

$$\left(\frac{1}{4}\right)^{1}\times 10^{1}r^{-3-2}s^{1+1}$$

Add the exponents -3 and -2.

$$\left(\frac{1}{4}\right)^{1}\times 10^{1}r^{-5}s^{1+1}$$

Add the exponents 1 and 1.

$$\left(\frac{1}{4}\right)^{1}\times 10^{1}\times \frac{1}{r^{5}}s^{2}$$

Multiply \frac{1}{4} times 10.

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

Differentiate w.r.t. r

$$-\frac{25s^{2}}{2r^{6}}$$