Solve z^4/z^7=

$$\frac { z ^ { 4 } } { z ^ { 7 } } =$$

Evaluate

$$\frac{1}{z^{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{z^{4}}{z^{7}}$$

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

$$z^{4-7}$$

Subtract 7 from 4.

$$z^{-3}$$

Differentiate w.r.t. z

$$-\frac{3}{z^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{4-7})$$

Do the arithmetic.

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

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}.

$$-3z^{-3-1}$$

Do the arithmetic.

$$-3z^{-4}$$