Solve v^5/v^10

$$\frac { v ^ { 5 } } { v ^ { 10 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{v^{5}}{v^{10}}$$

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

$$v^{5-10}$$

Subtract 10 from 5.

$$v^{-5}$$

Differentiate w.r.t. v

$$-\frac{5}{v^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{1}v^{5-10})$$

Do the arithmetic.

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

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}.

$$-5v^{-5-1}$$

Do the arithmetic.

$$-5v^{-6}$$