Solve a^3*a^2*a

$$a ^ { 3 } \cdot a ^ { 2 } \cdot a$$

Evaluate

$$a^{6}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{3}a^{2}a^{1}$$

Use the Multiplication Rule for Exponents.

$$a^{3+2+1}$$

Add the exponents 3 and 2.

$$a^{5+1}$$

Add the exponents 5 and 1.

$$a^{6}$$

Differentiate w.r.t. a

$$6a^{5}$$

Steps Using Definition of a Derivative

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

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

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

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

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

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

Subtract 1 from 6.

$$6a^{5}$$