Solve x^3/x^8

$$\frac { x ^ { 3 } } { x ^ { 8 } }$$

Evaluate

$$\frac{1}{x^{5}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{3}}{x^{8}}$$

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

$$x^{3-8}$$

Subtract 8 from 3.

$$x^{-5}$$

Differentiate w.r.t. x

$$-\frac{5}{x^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{3-8})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-5x^{-6}$$