Exploring Exponents: 0 and Negatives as Exponents

Lesson Plan - Get It!

Audio:

At this point, you should be familiar with the terms base and exponent.

Remember that the base is the number you will be multiplying by itself, and the exponent is the little ^tiny number that tells you how many times you will multiply the base by itself.

• Now, what happens if the exponent is 0?

Let's take a look at this video, What Do You Do With a Zero Exponent? Virtual Nerds: Real Help:

As you saw, any number to the 0 power is 1. It doesn't matter if it is x⁰, 4⁰, or even 1,000,0001⁰. Each of these will be equal to 1!

Great! We now know how to handle positive exponents and exponents of 0.

• But what about when we see a negative exponent?
• What do we do with that?

2^-3 = ?

When we have a negative exponent, we want to do the inverse (or opposite). Typically, when we see an exponent, we know we are going to be multiplying.

• So, what is the opposite of multiplication?

It's division. The negative exponent simply tells us how many times to divide by the base.

While it may sound tricky, I think you will like it. You are about to see that the negative exponent just means you are going to:

1. decide what the positive exponent would look like
2. take the reciprocal of the base with the above positive exponent

I have a feeling it will make more sense by looking at the example:

As you can see in this example, when you have negative exponents, you simply find the reciprocal and include the positive version of the exponent.

In the answer above, you can now do the math to find the final answer to be ¹/₈ (because 2 x 2 x 2 = 8).

Here are a few more examples to take a look at:

• Now, how about you try a few in the Got It? section?

You can feel free to look back at these examples at any point as a guide.

Remember, when dealing with negative exponents, you can simply decide what the positive version of the exponent would be and use it in the reciprocal.