Multiplying+Exponents

Look at the following 3 examples of multiplying exponents.


 * Example 1:**




 * Example 2:**




 * Example 3:**



**TASK: Based on the three examples above, make a prediction about what you think the rule is for multiplying exponents.**

When we multiply exponents there are two things we need to remember: 1. Multiply the coefficients 2. Multiply the exponents that have the same base by //keeping the base// and //adding the exponents//.


 * Why does adding the exponents work?**

Let's look at the first example above:

We can break this problem down into it's parts:





So then when we multiply the two terms we get:



Another way to write is.

Therefore, and the shortcut for this whole process is to keep the same base X and add the 2 + 5 to get the next exponent, 7.

**TASK: What do you think it means if you have a variable with no exponent? How would you multiply it? For example, how would you multiply ?**


 * What do we do if there isn't a power with the same base when we're multiplying?**

For example:

First, we multiply the coefficients:

Then, we multiply the powers with the same base:

The only thing we haven't multiplied yet is the "y," but there's no other "y" to multiply it with. So, we just bring the "y" down with the rest of the answer. Therefore, when we simplify the expression we get:

**TASK: Open the document and complete the practice problems. Turn the worksheet in during class**.