Solve c^frac{12{5}}divc^frac{14{5}}

$$c ^ { \frac { 12 } { 5 } } \div c ^ { \frac { 14 } { 5 } }$$

Evaluate

$$\frac{1}{c^{\frac{2}{5}}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{c^{\frac{12}{5}}}{c^{\frac{14}{5}}}$$

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

$$c^{\frac{12}{5}-\frac{14}{5}}$$

Subtract \frac{14}{5} from \frac{12}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$c^{-\frac{2}{5}}$$

Differentiate w.r.t. c

$$-\frac{2}{5c^{\frac{7}{5}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{1}{1}c^{\frac{12}{5}-\frac{14}{5}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{-\frac{2}{5}})$$

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}.

$$-\frac{2}{5}c^{-\frac{2}{5}-1}$$

Do the arithmetic.

$$-\frac{2}{5}c^{-\frac{7}{5}}$$