The zero exponent rule states that any term with an exponent of zero is equal to one. This lesson will go into the rule in more detail, explaining how it works and giving some examples.
Essentially, an exponent that is zero is equal to a variable to the power of an exponent times a variable to the negative power of the same exponent. For instance, x 2 times x-2 is equal to x 2 divided by x-2. Any number divided by itself is equal to one. Zero to the power of zero is a special case, however. Some mathematicians say that it ...
If a number (other than 0) has 0 as an exponent, it equals 1! It may be hard to believe but it is true, no matter what number. If a number has no exponent, there is basically an invisible 1 as the ...
Note: A lot of people get a little uneasy when they see 0, especially when that 0 is the exponent in some expression. After all, there seem to be so many rules about 0, and so many special cases where you're not allowed to do something.
Zero exponent. Any nonzero number raised to the 0 power is 1: = One interpretation of such a power is as an empty product. The case of 0 0 is more complicated, and the choice of whether to assign it a value and what value to assign may depend on context. For more details, see Zero to the power of zero.
The zero exponent rule basically says that any base with anexponent of zero is equal to one. For example: x^ 0 = 1 A negative exponent is equivalent to 1 over a positive exponent. x^1 = x x^ 0 = 1 ...
This automatically leads to the facts that 2 0 = 1, 3 0 = 1, and 10 0 = 1. We could do the same process for other numbers, too, and it would work the same way. So at least for all positive whole numbers a it is true that a 0 = 1. The video below shows the same idea: teaching zero exponent starting with a pattern.
Zero to any positive exponent equals zero. So, what happens when you have zero to the zero power? If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
0 : If the exponent is 0, then you get 1 (example 9 0 = 1) But what about 0 0? It could be either 1 or 0, and so people say it is "indeterminate". It All Makes Sense. My favorite method is to start with "1" and then multiply or divide as many times as the exponent says, then you will get the right answer, for example:
Discover a pattern that explains why any non-zero number to the zero power equals one. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.