Solve x^6/x^9

$$\frac { x ^ { 6 } } { x ^ { 9 } }$$

Evaluate

$$\frac{1}{x^{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{6}}{x^{9}}$$

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

$$x^{6-9}$$

Subtract 9 from 6.

$$x^{-3}$$

Differentiate w.r.t. x

$$-\frac{3}{x^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{6-9})$$

Do the arithmetic.

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

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}.

$$-3x^{-3-1}$$

Do the arithmetic.

$$-3x^{-4}$$