Solve x^2*x^5*x^1

$$x ^ { 2 } \times x ^ { 5 } \times x ^ { 1 }$$

Evaluate

$$x^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{2}x^{5}x^{1}$$

Use the Multiplication Rule for Exponents.

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

Add the exponents 2 and 5.

$$x^{7+1}$$

Add the exponents 7 and 1.

$$x^{8}$$

Differentiate w.r.t. x

$$8x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}x^{1})$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

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

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

$$8x^{8-1}$$

Subtract 1 from 8.

$$8x^{7}$$