Solve zdivz^11

$$z \div { z }^{ 11 }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$z^{1-11}$$

Subtract 11 from 1.

$$z^{-10}$$

Differentiate w.r.t. z

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{1-11})$$

Do the arithmetic.

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

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}.

$$-10z^{-10-1}$$

Do the arithmetic.

$$-10z^{-11}$$