How to Simplify Expressions with Exponents

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  • 0:05 Review of the…
  • 0:29 Practice Problem #1
  • 2:15 Practice Problem #2
  • 3:15 Practice Problem #3
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Lesson Transcript
Instructor: Kathryn Maloney

Kathryn teaches college math. She holds a master's degree in Learning and Technology.

In this video, we will put all of the exponent properties we have learned together. Don't let lots of numbers and letters confuse you! Simplifying exponents can be easy and fun!

Review of the Properties of Exponents

Let's review the exponent properties:

If you're having problems memorizing these properties, I suggest using flash cards. Flash cards are a fantastic and easy way to memorize topics, especially math properties.

Split up these expressions using multiplication after putting like terms on top of one another
Splitting Expressions with Multiplication

Practice Problem #1

So, let's get started!

Simplify is the same as reducing to lowest terms when we talk about fractions. Simplifying these terms using positive exponents makes it even easier for us to read.

Our first expression has x^3y^8 / y^3x^7. The first step I like to do is put the like terms on top of each other. On the top, I have x^3y^8. In the denominator, I want the xs over each other and the ys over each other, so I write x^7y^3.

My next step is to split these up using multiplication. This step is important when you first begin because you can see exactly what we are doing. Splitting the multiplication gives us x^3 / x^7 times y^8 / y^3.

Next step - look at each part individually. Since we have x^3 divided by x^7, we subtract their exponents. This gives us x^3-7. Since we have y^8 divided by y^3, we subtract their exponents. This gives us y^8-3. This will give us x^3-7, which is -4 and y^8-3, which is 5.

Solution to the first practice problem
Simplifying Expressions with Exponents Solution 1

Remember, we're simplifying using positive exponents, so we need to change x^-4. We know from our exponent properties that x^-4 is 1 / x^4 times y^5. Well, 5 is positive, so we don't need to change it.

My last step is to multiply. Our final, simplified answer is y^5 / x^4. This is our simplified answer with positive exponents.

Practice Problem #2

Let me show you another one. This time we have 5x^2y^9 / 15y^9x^4. Let's rewrite this with like terms over each other: 5/15 times x^2 / x^4 times y^9/y^9

We start at the beginning. 5/15 reduces to 1/3. Next, x^2 divided by x^4 is x^(2-4). y^9 divided by y^9 is y^(9-9). Let's keep simplifying. We have 1/3 times x^(2-4), which is -2, times y^(9-9), which is y^0. This gives us 1/3 times 1/x^2 times 1. Multiplying straight across, our final answer is 1/3x^2.

Steps in solving practice problem #2
Simplying Expressions with Exponents Problem 2

This is our answer simplified using positive exponents.

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