Radical & Rational Exponent

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The principal nth root of a is written as , where n is a positive integer greater than or equal to 2. In the radical expression, n is called the index of the radical. Radical expressions can also be written without using the radical symbol. We can use rational (fractional) exponents. The index must be a positive integer, and if the index n is even, then a cannot be negative.

We can also have rational exponents with numerators other than 1. In these cases, the exponent must be a fraction in lowest terms. We raise the base to a power and take an nth root. The numerator tells us the power and the denominator tells us the root.

All of the properties of exponents that we learned for integer exponents also hold for rational exponents.

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