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Zero Exponents

Many beginning students think it's weird that anything raised to the power of 0 is 1 . (I hear a lot of people say "It should be 0! ") You can use the product of powers property to show why this must be true.

7 0 × 7 1 = 7 (0+1) = 7 1

We know 7 1 =7 . So, this says that 7 0 ×7=7 . What number times 7 equals 7 ? If we try 0 , we have 0×7=7 . No good. The only number that works is 1 .

In general, for all real numbers a, a0 , we have:

a 0 =1

Note that 0 0 is undefined. (Click here to see why.)