Solve (-2z^3)(-4z^5)=

$$( - 2 z ^ { 3 } ) ( - 4 z ^ { 5 } ) =$$

Evaluate

$$8z^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$-2z^{8}\left(-4\right)$$

Multiply -2 and -4 to get 8.

$$8z^{8}$$

Differentiate w.r.t. z

$$64z^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-2z^{8}\left(-4\right))$$

Multiply -2 and -4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}z}(8z^{8})$$

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

$$8\times 8z^{8-1}$$

Multiply 8 times 8.

$$64z^{8-1}$$

Subtract 1 from 8.

$$64z^{7}$$