Solve z^2/z^3=

$$\frac { z ^ { 2 } } { z ^ { 3 } } =$$

Evaluate

$$\frac{1}{z}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{z^{2}}{z^{3}}$$

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

$$z^{2-3}$$

Subtract 3 from 2.

$$\frac{1}{z}$$

Differentiate w.r.t. z

$$-\frac{1}{z^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{z})$$

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}.

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

Do the arithmetic.

$$-z^{-2}$$