eli5: Why is x^0=1?

Question

I’m confused, shouldn’t it be 0?

In: Mathematics

Answer 1

The best way to see this is to use the addition and subtraction rules for multiplying and dividing exponents. Say you have x³/x² to do this you would use 3-2=1 and get x¹ which is just x. Now do the same but use x³/x³ we can see that this is the same numerator and denominator so we should get 1. Likewise if we use the rule from above we get 3-3=0. Thus x⁰=1.