Solve c^5/c^15

$$\frac { c ^ { 5 } } { c ^ { 15 } }$$

Evaluate

$$\frac{1}{c^{10}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{c^{5}}{c^{15}}$$

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

$$c^{5-15}$$

Subtract 15 from 5.

$$c^{-10}$$

Differentiate w.r.t. c

$$-\frac{10}{c^{11}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{1}{1}c^{5-15})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{-10})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-10c^{-10-1}$$

Do the arithmetic.

$$-10c^{-11}$$