Radical and Rational Exponents

A radical exponent is an exponent that is expressed as a fraction, where the numerator represents the power and the denominator represents the root. For example, $$x^{\frac{1}{2}}$$ is the square root of x.

The denominator of a rational exponent corresponds to the index of the radical expression.

@@ oot{3}{x} $$or$$ rac{1}{ oot{3}{x}}@@.

The index of the radical @@ oot{n}{x}@@ is n.

$$16^{\frac{1}{4}}$$ .

@@ oot{2}{x^3}@@.

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

Radical exponents can be expressed as rational exponents, and vice versa. For example, @@ oot{n}{x} $$can be written as$$ x^{rac{1}{n}}@@.

@@ oot{2}{x^5}@@.

$$x^2$$ .