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 divid... more  Nour Habona
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1 students helped

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11 days ago

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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167 students helped

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a month ago

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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11 students helped

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a month ago