Solve x^100/x^1000

$$\frac { x ^ { 100 } } { x ^ { 1000 } }$$

Evaluate

$$\frac{1}{x^{900}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{100}}{x^{1000}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$x^{100-1000}$$

Subtract 1000 from 100.

$$x^{-900}$$

Differentiate w.r.t. x

$$-\frac{900}{x^{901}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{100-1000})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-900})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-900x^{-900-1}$$

Do the arithmetic.

$$-900x^{-901}$$