Solve a^3*a*a^4

$$a ^ { 3 } \cdot a \cdot a ^ { 4 }$$

Evaluate

$$a^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{3}a^{1}a^{4}$$

Use the Multiplication Rule for Exponents.

$$a^{3+1+4}$$

Add the exponents 3 and 1.

$$a^{4+4}$$

Add the exponents 4 and 4.

$$a^{8}$$

Differentiate w.r.t. a

$$8a^{7}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{8})$$

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

$$8a^{8-1}$$

Subtract 1 from 8.

$$8a^{7}$$