Solve (-5z^4)(-2z^7)

$$( - 5 z ^ { 4 } ) ( - 2 z ^ { 7 } )$$

Evaluate

$$10z^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$-5z^{11}\left(-2\right)$$

Multiply -5 and -2 to get 10.

$$10z^{11}$$

Differentiate w.r.t. z

$$110z^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-5z^{11}\left(-2\right))$$

Multiply -5 and -2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}z}(10z^{11})$$

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

$$11\times 10z^{11-1}$$

Multiply 11 times 10.

$$110z^{11-1}$$

Subtract 1 from 11.

$$110z^{10}$$