Solve z^7/z^18

$$\frac { z ^ { 7 } } { z ^ { 18 } }$$

Evaluate

$$\frac{1}{z^{11}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{z^{7}}{z^{18}}$$

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

$$z^{7-18}$$

Subtract 18 from 7.

$$z^{-11}$$

Differentiate w.r.t. z

$$-\frac{11}{z^{12}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{7-18})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{-11})$$

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}.

$$-11z^{-11-1}$$

Do the arithmetic.

$$-11z^{-12}$$