Solve 100r^7s^3/10r^2s^5

$$\frac { 100 r ^ { 7 } s ^ { 3 } } { 10 r ^ { 2 } s ^ { 5 } }$$

Evaluate

$$\frac{10r^{5}}{s^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{100^{1}r^{7}s^{3}}{10^{1}r^{2}s^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{100^{1}}{10^{1}}r^{7-2}s^{3-5}$$

Subtract 2 from 7.

$$\frac{100^{1}}{10^{1}}r^{5}s^{3-5}$$

Subtract 5 from 3.

$$\frac{100^{1}}{10^{1}}r^{5}s^{-2}$$

Divide 100 by 10.

$$10r^{5}\times \frac{1}{s^{2}}$$

Differentiate w.r.t. s

$$-\frac{20r^{5}}{s^{3}}$$