Solve (x^9)(x^-3)(x^5)

$$( x ^ { 9 } ) ( x ^ { - 3 } ) ( x ^ { 5 } )$$

Evaluate

$$x^{11}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{9}x^{-3}x^{5}$$

Use the Multiplication Rule for Exponents.

$$x^{9-3+5}$$

Add the exponents 9 and -3.

$$x^{6+5}$$

Add the exponents 6 and 5.

$$x^{11}$$

Differentiate w.r.t. x

$$11x^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and -3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x^{5})$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{11})$$

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

$$11x^{11-1}$$

Subtract 1 from 11.

$$11x^{10}$$