Solve x^3*x^-2*x^6

$$x ^ { 3 } \cdot x ^ { - 2 } \cdot x ^ { 6 }$$

Evaluate

$$x^{7}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{3}x^{-2}x^{6}$$

Use the Multiplication Rule for Exponents.

$$x^{3-2+6}$$

Add the exponents 3 and -2.

$$x^{1+6}$$

Add the exponents 1 and 6.

$$x^{7}$$

Differentiate w.r.t. x

$$7x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}x^{6})$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

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

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

$$7x^{7-1}$$

Subtract 1 from 7.

$$7x^{6}$$