Types of Exponents and Types of Numbers
Before we get into doing operations with exponents lets make sure we understand the different types of exponents. There are many types of exponents as there are many types of numbers. I will list the basic ones that will provide you with the understanding to get through most problems. Keep in mind that negative and rational exponents can be combined.
Counting Numbers: An exponent that is number you can count like if you were counting sheep.
Zero exponents: An exponent that is zero.
Negative Integers: An exponent that is a negative number but is not a fraction.
Rational Numbers: An exponent that is a fraction
Counting Number Exponents
Lets start off by explaining the counting number exponents .
If you have an base raised to the exponent such that , then your are multiplying by , times.
What if you have an exponent that is zero. Well, if you just read the section on counting numbers and asked why there was a one out front, it will probably make sense now. If you have a base raised to the exponent , then you multiply by zero times, leaving you with . Any number to the exponent zero is just .
Negative Integer Exponents
When You have a base raised to a negative integer exponent such that you divide by , times.
Rational, or fractional exponents turn into radicals or roots. If there is an expression then you find the root of and then raise it to the exponent . is reffered to as the index which tells you which root you are taking.
The general rule is that