Solve a^2*a^3*(-a)

$$a ^ { 2 } \times a ^ { 3 } \times ( - a )$$

Evaluate

$$-a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$a^{5}\left(-a\right)$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

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

Differentiate w.r.t. a

$$-6a^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{5}\left(-a\right))$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}\left(-1\right))$$

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

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

Multiply 6 times -1.

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

Subtract 1 from 6.

$$-6a^{5}$$