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The simple way to reason it is this: think backwards. Say I tell you that 210=1024. Given this how would you find 29? You would never want to multiply the whole thing out again. You would probably divide 210 by 2. What's 23? 8. What is 22? divide that last answer by 2 to get 8/2 = 4. What is 21? divide the last answer by 2 to get 4/2 = 2. What is 20? divide the last answer by 2 to get 2/1 = 1.
In higher mathematics, the reason comes from the definition. Mathematicians define a0 = 1 and then they define an+1 as an * a. Let me think of an example. If we define 20=1, then what is 21? 21= 20+1= 20*2 (this is because we defined it this way an*a = an+1). = 1*2 = 2. We can similarly define every exponent in this way by using the one below it. Mathematicians call this a definition by induction.
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What is zero exponent?
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 exponent, so the number would be equal to itself. Zero with the exponent zero is meaningless.
Any nonzero number raised to the power of zero is equal to?
Any nonzero number raised to the power of zero is equal to one (1).By definition.
Why is the answer always one when the exponent is zero?
because it will ALWAYS = 1
Can you have more than one exponent on top of a number?
Yes, you can, but it starts getting complicated. You can, for example have a number raised to an exponent that is itself a number raised to an exponent, or you can have a number raised to an exponent and the result raised to another exponent.
What is an irrational exponent?
It means that it is an exponent, and that it is not a rational number - i.e., one that can be written as a fraction of two integers.
