Solve x^-2*x^-2*x^-2

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

Evaluate

$$\frac{1}{x^{6}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

Use the Multiplication Rule for Exponents.

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

Add the exponents -2 and -2.

$$x^{-4-2}$$

Add the exponents -4 and -2.

$$x^{-6}$$

Differentiate w.r.t. x

$$-\frac{6}{x^{7}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -2 and -2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-4}x^{-2})$$

To multiply powers of the same base, add their exponents. Add -4 and -2 to get -6.

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

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

$$-6x^{-6-1}$$

Subtract 1 from -6.

$$-6x^{-7}$$