Solve a*a^2*a^5

$$a \cdot a ^ { 2 } \cdot a ^ { 5 }$$

Evaluate

$$a^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{1}a^{2}a^{5}$$

Use the Multiplication Rule for Exponents.

$$a^{1+2+5}$$

Add the exponents 1 and 2.

$$a^{3+5}$$

Add the exponents 3 and 5.

$$a^{8}$$

Differentiate w.r.t. a

$$8a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{3}a^{5})$$

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

$$8a^{7}$$