Solve -7z^4(-3z^8)

$$- 7 z ^ { 4 } ( - 3 z ^ { 8 } )$$

Evaluate

$$21z^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$-7z^{12}\left(-3\right)$$

Multiply -7 and -3 to get 21.

$$21z^{12}$$

Differentiate w.r.t. z

$$252z^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-7z^{12}\left(-3\right))$$

Multiply -7 and -3 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}z}(21z^{12})$$

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

$$12\times 21z^{12-1}$$

Multiply 12 times 21.

$$252z^{12-1}$$

Subtract 1 from 12.

$$252z^{11}$$