Solve c^-3*c^8*c^-8

$$c ^ { - 3 } \cdot c ^ { 8 } \cdot c ^ { - 8 }$$

Evaluate

$$\frac{1}{c^{3}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$c^{-3}c^{8}c^{-8}$$

Use the Multiplication Rule for Exponents.

$$c^{-3+8-8}$$

Add the exponents -3 and 8.

$$c^{5-8}$$

Add the exponents 5 and -8.

$$c^{-3}$$

Differentiate w.r.t. c

$$-\frac{3}{c^{4}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and 8 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{5}c^{-8})$$

To multiply powers of the same base, add their exponents. Add 5 and -8 to get -3.

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

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

$$-3c^{-3-1}$$

Subtract 1 from -3.

$$-3c^{-4}$$