Common Core Math For Parents For Dummies with Videos Online
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Common Core math students start to work with exponents in eighth grade. In algebra, you can think of exponentiation as repeated multiplication. The following analogy will help you understand the significance of this.

You know that


because there are 12 things in 4 groups of 3. If you didn't know the product


you could find it in several ways. You could lay out 4 groups of 3 things and count them one by one, for example. Or you could use the associative property of multiplication, which means that to find


you can either multiply a and b first, or you can multiply b and c first — the final product is the same either way. Using the associative property, you could think of


is twice as much as


Finally, you could think


That is, one way to compute products is by using repeated addition.

It's the same with exponents:


From 4 and 3, you compute a third number, 64. Just as you can compute


by using repeated addition, you can compute


using repeated multiplication:


But there are other ways too, and these ways depend on properties of exponentiation as an operation. You can double


to get


using the associative property of multiplication, and properties of exponentiation allow you to relate


These properties are known as rules for operating with exponents.

Three major rules appear in eighth grade. In the following statements, A is presumed to be a positive number:


You can understand these rules better by way of examples. You can see the first rule, that


by thinking of


Six threes are multiplied. The second rule you can see by thinking about


Eight threes are multiplied together. The third rule is the logical consequence of the first rule, and of the fact that


when A is any positive number. Here's why:


by the first rule. Then


has to be the reciprocal of


Each of these rules is useful going in both directions. You don't have to view these equations as machines that transform the left-hand side into the right-hand side. Instead, each side of each equation has the same value as the other side. Sometimes you have something that looks like this:


and it's useful to write it as


Sometimes it goes the other way around. What matters is the equivalence — or sameness — of both sides of each equation.

About This Article

This article is from the book:

About the book author:

Christopher Danielson, PhD, is a leading curriculum writer, educator, math blogger, and author interpreting research for parents and teachers across the country from his home base at Normandale Community College in Minnesota.

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