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 ab=ca^{b}=c we refer to aa as the base, bb as the exponent and cc as the argument.

If the exponent bb is an even number then the argument cc will always be positive, whether aa is positive or negative.

If the exponent bb is an odd number then the argument cc will always be positive if aa is positve, and negative if aa is negative.

If the exponentbb 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
4 years, 7 months ago

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