Solve z^7/z^2=

$$\frac { z ^ { 7 } } { z ^ { 2 } } =$$

Evaluate

$$z^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{z^{7}}{z^{2}}$$

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

$$z^{7-2}$$

Subtract 2 from 7.

$$z^{5}$$

Differentiate w.r.t. z

$$5z^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{7-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{5})$$

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}.

$$5z^{5-1}$$

Do the arithmetic.

$$5z^{4}$$