Solve c^4*c^7/c^3

$$\frac { c ^ { 4 } \cdot c ^ { 7 } } { c ^ { 3 } }$$

Evaluate

$$c^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{c^{11}}{c^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 11 to get 8.

$$c^{8}$$

Differentiate w.r.t. c

$$8c^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c^{11}}{c^{3}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 11 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{8})$$

The derivative of ax^{n} is nax^{n-1}.

$$8c^{8-1}$$

Subtract 1 from 8.

$$8c^{7}$$