Solve z^6/z^4

$$\frac { z ^ { 6 } } { z ^ { 4 } }$$

Evaluate

$$z^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{z^{6}}{z^{4}}$$

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

$$z^{6-4}$$

Subtract 4 from 6.

$$z^{2}$$

Differentiate w.r.t. z

$$2z$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{6-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$2z^{1}$$

For any term t, t^{1}=t.

$$2z$$