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This derives from one of the laws of indices which states that, for any x (not = 0),

xa * xb = xa+b

Put b = 0

Then xa * x0 = xa+0 = xa (because a + 0 = a)

But that means that x0 is the multiplicative identity. And since that is unique, and equal to 1,

x0 = 1.

This is true for all x.

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โˆ™ 2011-12-16 15:16:13
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Q: Why any number raised to power zero is 1?
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