Solve x^7x^-5x^3

$${ x }^{ 7 } { x }^{ -5 } { x }^{ 3 }$$

Evaluate

$$x^{5}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{7}x^{-5}x^{3}$$

Use the Multiplication Rule for Exponents.

$$x^{7-5+3}$$

Add the exponents 7 and -5.

$$x^{2+3}$$

Add the exponents 2 and 3.

$$x^{5}$$

Differentiate w.r.t. x

$$5x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and -5 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{3})$$

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

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

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

$$5x^{5-1}$$

Subtract 1 from 5.

$$5x^{4}$$