Solve x^3x^0x^-5

$${ x }^{ 3 } { x }^{ 0 } { x }^{ -5 }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{3}x^{0}x^{-5}$$

Use the Multiplication Rule for Exponents.

$$x^{3-5}$$

Add the exponents 3 and -5.

$$x^{-2}$$

Differentiate w.r.t. x

$$-\frac{2}{x^{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}x^{-5})$$

To multiply powers of the same base, add their exponents. Add 3 and -5 to get -2.

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

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

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

Subtract 1 from -2.

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