In this lesson, we’re going to look at A to the power of zero. You might already recognize A to the power of one as another way of writing A, or nine to the one or simply nine. But what happens when we have A to the power of zero, or nine to the pair of zero? What is the value of anything raised to the power of zero? I’d like to look at some regular division questions to help us to solve this question. I’m sure you know that 274 divided by 274 is one. Similarly, 19AB divided by 19AB is also one. Whenever you divide anything by itself, the result that you get is always one. There’s one exception to this rule. You can’t divide zero by zero. That’s meaningless.
Now, based on the principle that anything divided by itself equals one, what do we get when we divide A to the M by A to the M? Once again, the answer is one. But now let’s look at A to the M divided by A to the M again, and this time use the index laws to solve the question. Remember when dividing by terms with the sign base, we subtract the indices. Here, we have A to the M divided by A to the M. That equals A to the M, minus same which equals A to the zero. But we already know that A to the M divided by A to the M gave us one. This means that A to the zero must equal one. We’ll write this down as a general rule. A to the power of zero equals one where A cannot equal zero. There is no meaning to zero raised to the power of zero. You can check this new rule for yourself on your calculator. Enter any number, raise it to the power of zero and see what you get. For example, three to the power of zero equals one. Twenty-seven to the power of zero equals one.