Solve 7a^2*(-4a^4)=

$$7 a ^ { 2 } \times ( - 4 a ^ { 4 } ) =$$

Evaluate

$$-28a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$7a^{6}\left(-4\right)$$

Multiply 7 and -4 to get -28.

$$-28a^{6}$$

Differentiate w.r.t. a

$$-168a^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{6}\left(-4\right))$$

Multiply 7 and -4 to get -28.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-28a^{6})$$

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

$$6\left(-28\right)a^{6-1}$$

Multiply 6 times -28.

$$-168a^{6-1}$$

Subtract 1 from 6.

$$-168a^{5}$$