Solve v^14/v^6

$$\frac { v ^ { 14 } } { v ^ { 6 } }$$

Evaluate

$$v^{8}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{v^{14}}{v^{6}}$$

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

$$v^{14-6}$$

Subtract 6 from 14.

$$v^{8}$$

Differentiate w.r.t. v

$$8v^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{1}v^{14-6})$$

Do the arithmetic.

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

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}.

$$8v^{8-1}$$

Do the arithmetic.

$$8v^{7}$$