Solve z^6z^-4z^-3=

$${ z }^{ 6 } { z }^{ -4 } { z }^{ -3 } =$$

Evaluate

$$\frac{1}{z}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$z^{6}z^{-4}z^{-3}$$

Use the Multiplication Rule for Exponents.

$$z^{6-4-3}$$

Add the exponents 6 and -4.

$$z^{2-3}$$

Add the exponents 2 and -3.

$$\frac{1}{z}$$

Differentiate w.r.t. z

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and -4 to get 2.

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

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

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

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

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

Subtract 1 from -1.

$$-z^{-2}$$