Solve z*z^2*z^4

$$z \cdot z ^ { 2 } \cdot z ^ { 4 }$$

Evaluate

$$z^{7}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$z^{1}z^{2}z^{4}$$

Use the Multiplication Rule for Exponents.

$$z^{1+2+4}$$

Add the exponents 1 and 2.

$$z^{3+4}$$

Add the exponents 3 and 4.

$$z^{7}$$

Differentiate w.r.t. z

$$7z^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{3}z^{4})$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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

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

$$7z^{7-1}$$

Subtract 1 from 7.

$$7z^{6}$$