Solve (-5z^5)(6z^6)=

$$( - 5 z ^ { 5 } ) ( 6 z ^ { 6 } ) =$$

Evaluate

$$-30z^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$-5z^{11}\times 6$$

Multiply -5 and 6 to get -30.

$$-30z^{11}$$

Differentiate w.r.t. z

$$-330z^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-5z^{11}\times 6)$$

Multiply -5 and 6 to get -30.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-30z^{11})$$

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

$$11\left(-30\right)z^{11-1}$$

Multiply 11 times -30.

$$-330z^{11-1}$$

Subtract 1 from 11.

$$-330z^{10}$$