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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
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.
Asked by Liam