Any number to the power zero is 1 - except 0 to the power zero, which is undefined.
Consider this sequence:
23 = 8
22 = 4
21 = 2
20 = ???
How do you complete this sequence? Note that at the right, each number is half the previous number. Therefore, 1 looks like the logical choice. Defining x0 = 1 extends the validity of several formulae, including the multiplication of powers: xa times xb = xa+b.
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