Solve a^4*a*a^4=

$$a ^ { 4 } \cdot a \cdot a ^ { 4 } =$$

Evaluate

$$a^{9}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{4}a^{1}a^{4}$$

Use the Multiplication Rule for Exponents.

$$a^{4+1+4}$$

Add the exponents 4 and 1.

$$a^{5+4}$$

Add the exponents 5 and 4.

$$a^{9}$$

Differentiate w.r.t. a

$$9a^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

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

$$9a^{8}$$