Question Video: Evaluating a Decimal of Zero Exponent Mathematics • 8th Grade

Evaluate 0.2⁰.

01:50

Video Transcript

Evaluate 0.2 to the power of zero.

When it comes to answering a question like this, there’s one very important rule that we should remember when we’re working with an exponent of zero. And that is that any base with an exponent of zero is equal to one. We might even see this written as 𝑥 to the power of zero is equal to one. Therefore, in this question, 0.2 to the power of zero is equal to one. Notice that it doesn’t matter how large the starting value is. For example, we could have three million to the power of zero, and that would still give us an answer of one.

Let’s cover quickly why this fact is true. Let’s say that we have this problem 𝑑 to the power of six divided by 𝑑 to the power of six. To Answer this problem, we would use one of the rules of exponents that 𝑥 to the power of 𝑎 divided by 𝑥 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎 minus 𝑏. So in this example problem, the 𝑑 to the power of six divided by 𝑑 to the power of six is equal to 𝑑 to the power of six minus six. Since six minus six is zero, that leaves us with 𝑑 to the power of zero.

So how does that help us? Well, let’s look back at this problem. We have this value 𝑑 to the power of six divided by 𝑑 to the power of six. And what do we know about any value divided by itself? Well, it’s one. And so we have shown that any value with an exponent of zero is also equal to one. So we’ve demonstrated that the answer to 0.2 to the power of zero is one.

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