Solve z^3*z^3*z=

$$z ^ { 3 } \cdot z ^ { 3 } \cdot z =$$

Evaluate

$$z^{7}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$z^{3}z^{3}z^{1}$$

Use the Multiplication Rule for Exponents.

$$z^{3+3+1}$$

Add the exponents 3 and 3.

$$z^{6+1}$$

Add the exponents 6 and 1.

$$z^{7}$$

Differentiate w.r.t. z

$$7z^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

To multiply powers of the same base, add their exponents. Add 6 and 1 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.

$$7z^{6}$$