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Asked by Antima

# Can anyone explain why 0's exponent any number is 1?

Another way to explain why this is the rule, is by using a pattern lets use the number 2 and answers using both positive and negative exponents. 2^4 = 16 2^3 = 8 2^2 = 4 2^1 = 2 2^0 =?? 2^ -1 = 1/2 2^ - 2 = 1/4 2^ - 3 = 1/8 2^ - 4 = 1/16 Moving down the list you divide by 2 every time. Or going upward you multiply by 2 every step. When you get to 2^0 following the pattern going down and dividing by 2 this means: 2^0 = 2^1 ÷ 2 = 1 Hope this helps 😊  Nour Habona
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415 students helped

If we look at the following equation: (x^0)(x^b)=x^(0+b), by the rules of indices but simplifying we have x^(0+b)= x^b so we have, (x^0)(x^b)=x^b and dividing by x^b (given that x isn't 0) gives x^0 = 1  Zahra Bashir
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11.1k students helped

The easiest way I can explain it is by using Laws of Exponents. x^2 ÷ x^2 is equal to x^(2-2). This equals x^0. But we also know anything divided by itself is equal to 1. So put the two laws together and then we can say anything to the power of 0 equals 1.  Jenny Chakanyuka
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905 students helped

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