Solve v^5/v^2

$$\frac { v ^ { 5 } } { v ^ { 2 } }$$

Evaluate

$$v^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{v^{5}}{v^{2}}$$

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

$$v^{5-2}$$

Subtract 2 from 5.

$$v^{3}$$

Differentiate w.r.t. v

$$3v^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{1}v^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{3})$$

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}.

$$3v^{3-1}$$

Do the arithmetic.

$$3v^{2}$$