Solve a*a^3*a^5

$$a \cdot a ^ { 3 } \cdot a ^ { 5 }$$

Evaluate

$$a^{9}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{1}a^{3}a^{5}$$

Use the Multiplication Rule for Exponents.

$$a^{1+3+5}$$

Add the exponents 1 and 3.

$$a^{4+5}$$

Add the exponents 4 and 5.

$$a^{9}$$

Differentiate w.r.t. a

$$9a^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}a^{5})$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9})$$

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

$$9a^{9-1}$$

Subtract 1 from 9.

$$9a^{8}$$