Solve v^20/v^30

$$\frac { v ^ { 20 } } { v ^ { 30 } }$$

Evaluate

$$\frac{1}{v^{10}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{v^{20}}{v^{30}}$$

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

$$v^{20-30}$$

Subtract 30 from 20.

$$v^{-10}$$

Differentiate w.r.t. v

$$-\frac{10}{v^{11}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{1}v^{20-30})$$

Do the arithmetic.

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

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}.

$$-10v^{-10-1}$$

Do the arithmetic.

$$-10v^{-11}$$