# Even, Odd and Fractional Exponents. Continuing my set of notes on exponents here are some things to consider about exponents. If there is a relationship such that $a^{b}=c$ we refer to $a$ as the base, $b$ as the exponent and $c$ as the argument.

If the exponent $b$ is an even number then the argument $c$ will always be positive, whether $a$ is positive or negative.

If the exponent $b$ is an odd number then the argument $c$ will always be positive if $a$ is positve, and negative if $a$ is negative.

If the exponent$b$ is a fraction it results in a radical or "root".

Even roots such as the square root will always be positive. The positive root is called the principal root. This stems from the fact that a negative number times a negative number results in a positive number. Essentially the square roots of negative numbers are imaginary numbers.

Odd roots can be negative or positive. The cube root of a negative number will be a negative number, and the cube root a positive number will be positive. Note by Brody Acquilano
5 years, 7 months ago

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