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Simplifying Expressions with Exponents - Problem 1

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

To simplify a variable expression with exponents, start by writing out all the exponents. For example, write out x^4 as x x x x. Next, cancel out everything you can from the numerator and denominator. Then multiply the remaining variables and constants. The result is the expression in simplest form.

The most sure fire way to approach a problem with exponents is to write everything out. Like for example this whole fraction’s being squared, so that means times itself. I’m going to write 2x to the 4th over xyz squared times itself.

Next thing I’m going to do is go through and write out every single letter so I can cancel out things that are the same on top and bottom. On top I’ll have 2x to the 4th times 2x to the 4th. On the bottom I’ll have xyzz, and then that same thing again xyzz.

The last step once you write it out is kind of fun. You get to cross out anything that is the same on top and bottom. It’s like reducing a fraction when you have the same factors on top and bottom like that x and that x can go and that x and that x can go, that was it that wasn’t too much fun because I didn’t have any much crossing out to do, but you will.

Okay let’s simplify the top, 2×2=4 dealing with my constants first. Then I have 1, 2, 3, 4, 5, 6 Xs being multiplied together so that’s like x to the 6th. On the bottom I have y times itself and then I have 1, 2, 3, 4 Zs being multiplied. Be really careful that you don’t write that as 4z, z times itself 4 times is written as z to the 4th. This is my final answer, and I know it’s in most simplified form because I don’t have any constants on top and bottom that could be reduced, nor do I have the same letter showing up on top and bottom, and I also don’t have any negative exponents. So this is equal to that just in most simplified form.

Again what I did was write it out twice because it was squared, then I wrote out every single letter so I could cancel things out that were the same on top and bottom of that fraction.

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