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# 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
1 year, 11 months ago