Solve x^3/x^18

$$\frac{ { x }^{ 3 } }{ { x }^{ 18 } }$$

Evaluate

$$\frac{1}{x^{15}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{3}}{x^{18}}$$

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

$$x^{3-18}$$

Subtract 18 from 3.

$$x^{-15}$$

Differentiate w.r.t. x

$$-\frac{15}{x^{16}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{3-18})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-15})$$

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}.

$$-15x^{-15-1}$$

Do the arithmetic.

$$-15x^{-16}$$