Solve x^8/x^3

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

Evaluate

$$x^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$x^{8-3}$$

Subtract 3 from 8.

$$x^{5}$$

Differentiate w.r.t. x

$$5x^{4}$$

Solution Steps

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

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

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.

$$5x^{4}$$