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Hi, students often ask why is x to the zero power or any number to the zero power one?
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And there's a bunch of different ways you can show it.
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I'm going to show one that doesn't require a lot of algebra because there are some really
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great ways to show this algebraically when you know the lots of exponents.
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But just for our purposes today, we're just going to show kind of a logical deduction
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of unfolding of y sum number to the zero power one.
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So I'm going to demonstrate it with three.
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Three to the zero power is one.
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So if you look at this patterning, we know that 27 is equal to 3 cubed.
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So 3 times 3 is 9 and 9 times 3 is 27.
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So 3 to the third power is 27.
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9 is equal to 3 squared, 3 times 3 is 9.
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So these are all things that we know and agree upon.
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3 is equal to 3 to the first power.
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So y is that the 3 to the zero power is one and not zero.
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That's why students are constantly wondering.
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So the way I like to think about it is if I were just looking at here, how can I go backwards?
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So if I divide by 3, 27 divided by 3 gives me 9, which is 3 squared.
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And you can see I went down by an exponent, I went down minus 1.
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I subtracted 1.
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If I do this again and I divide by 3, 9 divided by 3 is 3.
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And I also go down and I take one off the exponent.
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I'm going down by a factor of 3.
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If I do this again and I divide by 3, 3 divided by 3 is 1.
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And I also go down by negative 1.
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So 1 minus 1 is zero.
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So looking at it as a pattern base, you can see that this is going to make sense.