Solve 2z^-5div4z^3

$$2 z ^ { - 5 } \div 4 z ^ { 3 }$$

Evaluate

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

Solution Steps

Divide 2z^{-5} by 4 to get \frac{1}{2}z^{-5}.

$$\frac{1}{2}z^{-5}z^{3}$$

To multiply powers of the same base, add their exponents. Add -5 and 3 to get -2.

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

Differentiate w.r.t. z

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

Steps Using Definition of a Derivative

Divide 2z^{-5} by 4 to get \frac{1}{2}z^{-5}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{2}z^{-5}z^{3})$$

To multiply powers of the same base, add their exponents. Add -5 and 3 to get -2.

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

The derivative of ax^{n} is nax^{n-1}.

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

Multiply -2 times \frac{1}{2}.

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

Subtract 1 from -2.

$$-z^{-3}$$