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.

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