Solve x^2xx^-12

$$x ^ { 2 } x x ^ { - 12 }$$

Evaluate

$$\frac{1}{x^{9}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{2}x^{1}x^{-12}$$

Use the Multiplication Rule for Exponents.

$$x^{2+1-12}$$

Add the exponents 2 and 1.

$$x^{3-12}$$

Add the exponents 3 and -12.

$$x^{-9}$$

Differentiate w.r.t. x

$$-\frac{9}{x^{10}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}x^{-12})$$

To multiply powers of the same base, add their exponents. Add 3 and -12 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-9})$$

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

$$-9x^{-9-1}$$

Subtract 1 from -9.

$$-9x^{-10}$$