Solve a^6*a^8*a^10

$$a ^ { 6 } \times a ^ { 8 } \times a ^ { 10 }$$

Evaluate

$$a^{24}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{6}a^{8}a^{10}$$

Use the Multiplication Rule for Exponents.

$$a^{6+8+10}$$

Add the exponents 6 and 8.

$$a^{14+10}$$

Add the exponents 14 and 10.

$$a^{24}$$

Differentiate w.r.t. a

$$24a^{23}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{14}a^{10})$$

To multiply powers of the same base, add their exponents. Add 14 and 10 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{24})$$

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

$$24a^{24-1}$$

Subtract 1 from 24.

$$24a^{23}$$