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Multiplication and Division Properties of Exponents - Problem 3

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

When simplifying expressions with exponents, keep in mind the rules of exponents as well as order of operations. Remember that when a value inside parenthesis is raised to an exponent, everything in that parenthesis must be raised to that power. Keep in mind order of operations (PEMDAS).

All right guys this is a challenging exponents simplification problem that uses the properties of division and multiplication. Let’s go to it.

I’m going to go ahead and write out all of this stuff so that I’m assured I’m going to get the right answer without jumbling the properties of exponents in my head. On top it starts with 3², there it is. Then I need 3x times itself three times. So 3x times itself three times. All of that is the top written out. If you want to you can use parentheses like I did to show the groupings or we can also write this using the little dots because in Math the little dots also mean multiply, so if you wanted to you might have written it like this; times, times, times, okay.

Then on the bottom of my fraction I have 3 and then I need x to the 5th. Be really careful, 3 x to the 5th is different from (3x) to the 5th. This 5 only applies to the x there. So when I write out my denominator I’m going to have 3 and then 5 Xs. Okay so let’s start simplifying stuff.

On top and bottom I have some things that are the same so they can be what we call reduced to the value of 1 like 3/3 is equal to 1. Here is an x/x that’s equal to 1. There’s another x/x and there is another x/x. Everything that got crossed out is in the process of reducing. Here’s what’s left. I have on top; 1, 2, 3, 4. I have 3 to the 4th on top. What else do I have? No Xs so the top is all done. Let’s look at the bottom. On the bottom, that 3 is gone. All those Xs are gone, all I have left is x².

That’s my simplified answer and I’m pretty darn sure it’s right because I wrote everything out. The only place where you might make a mistake using this method is in the reducing just be careful that you cross out things that are exactly the same on top and bottom when the stuff’s being multiplied.

You guys can do that and keep track of writing out all of your exponents, I promise you you’re going to do really well in this chapter, bring home the A+ for your refrigerator.

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