Solve 2^3c^2/2^2c

$$\frac { 2 ^ { 3 } c ^ { 2 } } { 2 ^ { 2 } c }$$

Evaluate

$$2c$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{2^{3}c^{2}}{2^{2}c^{1}}$$

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

$$2^{3-2}c^{2-1}$$

Subtract 2 from 3.

$$2^{1}c^{2-1}$$

Raise 2 to the power 1.

$$2c^{2-1}$$

Subtract 1 from 2.

$$2c^{1}$$

For any term t, t^{1}=t.

$$2c$$

Differentiate w.r.t. c

$$2$$

Steps Using Definition of a Derivative

Cancel out 2^{2}c in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(2c)$$

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

$$2c^{1-1}$$

Subtract 1 from 1.

$$2c^{0}$$

For any term t except 0, t^{0}=1.

$$2\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2$$