Solve 20v^8/5v

$$\frac { 20 v ^ { 8 } } { 5 v }$$

Evaluate

$$4v^{7}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{20^{1}v^{8}}{5^{1}v^{1}}$$

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

$$\frac{20^{1}v^{8-1}}{5^{1}}$$

Subtract 1 from 8.

$$\frac{20^{1}v^{7}}{5^{1}}$$

Divide 20 by 5.

$$4v^{7}$$

Differentiate w.r.t. v

$$28v^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{20}{5}v^{8-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}v}(4v^{7})$$

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}.

$$7\times 4v^{7-1}$$

Do the arithmetic.

$$28v^{6}$$