Did You Know, Why Raising Anything To a Zero Power Equals One?

Well, we’ve encountered this law of exponent in Algebra that any number raised to an exponent of zero is equal to one, that is a0 =1. Why is this so?

For some students when asked why just say, “It’s just the rule.”

However for us who wanted a more detailed answer and meaning to this problem, this answer is not sufficient.

But recall that there is also a rule in exponents which states that when a number a with an exponent of m is divided by the same number a with an exponent of n is equal to the number a with the exponent of m minus n, or in formula we have:

am /an = am-n


And when does the exponent of a be equal to zero? Certainly, it is when m = n. For instance, if we let a = 3, and m = 2 and n = 2, we have

am /an

32 /32


However, we noticed that if m =n, the resulting exponent becomes zero and also if m = n, we came up dividing a number by itself, which is equal to one. Therefore we can say that any number whose exponent is zero is equal to one because it’s just like dividing a number by itself, and dividing a number by itself is always equal to one.