Solve x^8*x^2*x^6

$$x ^ { 8 } \times x ^ { 2 } \times x ^ { 6 }$$

Evaluate

$$x^{16}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{8}x^{2}x^{6}$$

Use the Multiplication Rule for Exponents.

$$x^{8+2+6}$$

Add the exponents 8 and 2.

$$x^{10+6}$$

Add the exponents 10 and 6.

$$x^{16}$$

Differentiate w.r.t. x

$$16x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10}x^{6})$$

To multiply powers of the same base, add their exponents. Add 10 and 6 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{16})$$

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

$$16x^{16-1}$$

Subtract 1 from 16.

$$16x^{15}$$