Solve x^0*x^-5*x^4

$${ x }^{ 0 } \times { x }^{ -5 } \times { x }^{ 4 }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{0}x^{-5}x^{4}$$

Use the Multiplication Rule for Exponents.

$$x^{-5+4}$$

Add the exponents -5 and 4.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 0 and -5 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-5}x^{4})$$

To multiply powers of the same base, add their exponents. Add -5 and 4 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.

$$-x^{-2}$$