Why Is A Number Raised To The Power Zero = One?

This fundamental question questions your fundamentals!

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If you are the typical person, you have the general understanding that any number raised to the power zero equals one. When we try out a few examples on a calculator, our knowledge is reaffirmed. And because of this, most of us seldom question: Why? Very few of us actually understand why a number raised to the power zero equals one. In this article, I try to explain why exponentiation (a number raised to the power of another number) works this way by solving easy, incremental puzzles that anyone can understand. Furthermore, there is one exception where this cannot be applied. So, it is mathematically wrong to say that any number raised to the power zero equals one. We’ll also touch upon this point shortly towards the end.

What is Exponentiation?

Let us begin with understanding exponentiation. It is easier to take a look at examples first and then move on to the theoretical reasoning behind them. Consider the example: 2³ = 8. Here, the base (2) occurs in a multiplicative series the exponent (3) Number of times: 2*2*2. The answer is then the result of multiplication. The key point to note here is the process of exponentiation is first resolved into a multiplicative series. Then, carrying out the multiplication…