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.

#Algebra #Exponents #RulesOfExponents

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$