Solve x^3*x^-3*x^-1=

$${ x }^{ 3 } \times { x }^{ -3 } \times { x }^{ -1 } =$$

Evaluate

$$\frac{1}{x}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{3}x^{-3}\times \frac{1}{x}$$

Use the Multiplication Rule for Exponents.

$$x^{3-3-1}$$

Add the exponents 3 and -3.

$$\frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Definition of a Derivative

Multiply x^{3} and x^{-3} to get 1.

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

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

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

Subtract 1 from -1.

$$-x^{-2}$$