Solve x^6/x^10

$$\frac{ { x }^{ 6 } }{ { x }^{ 10 } }$$

Evaluate

$$\frac{1}{x^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{6}}{x^{10}}$$

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

$$x^{6-10}$$

Subtract 10 from 6.

$$x^{-4}$$

Differentiate w.r.t. x

$$-\frac{4}{x^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{6-10})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-4})$$

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}.

$$-4x^{-4-1}$$

Do the arithmetic.

$$-4x^{-5}$$