Factor and simplify each algebraic expression.

Question

[12 x^{- \frac{1}{2}} + 6 x^{- \frac{3}{2}}]

Accepted Answer

Hi there. This problem says when I performed Factory Ization and simplified to give an expression 44 X. The power of negative one third plus 22 X. The power of negative five thirds. Let's go ahead and look at this equation. So I'm gonna write it out again have X. And negative one third plus 22 X. To the negative five thirds. So the first step we kinda want to see is can we factor out the constants? So we have 44 and 22 for our constants for these expressions. So is there a thing we can factor out out of both of them? I would say there is because we have 44 and 22. Let's say we try factoring out a 22 out of these. So we have 22. Take that out. We get to X to the negative one third Plus X to the -5/3. So we took out the 22 but we also need to take out some of the exponents. So we have two X. And negative one third plus X. To the negative five flirts. A good choice here is to try and factor out the lowest exponent out of both exponents here. In that case that is our negative 1/3. Let's try to factor out an X to the -1 3rd. So I'll go and take out X two negative one third. 22 X negative one third two Plus whatever this will be over here. I want a fragile and X 9 to 1 third from the X two negative five thirds. So you have X. And negative five thirds. We factor out we're pretty much dividing Rx the five thirds by X. The native one third. So pretty much taking out when they're negative excavated. 1/3 out of the excavated 5/3. So if you remember from the lesson but um multiplying dividing exponents. When you divide exponents, you're going to subtract the exponents in exponent area. So what do I mean by that Is we're gonna have X. to the negative 5/3. The division is going to make our exponent minus and then our exponent at the bottom negative 1/3. When I do that, I will get X to the negative 5/ Plus 1 3rd at the top Many. We get X to the negative 4/3. So we go back to our main problem. We have X To the negative 4/3 here. So that should be our factory ization. We look over at our answers. We see that answer. A. Is this answer 22 X to the negative one third times two plus X. To the negative four thirds. All right. I hope that help you solve the problem. Thank you for watching

Factor and simplify each algebraic expression. $[12 x^{- \frac{1}{2}} + 6 x^{- \frac{3}{2}}]$

Key Concepts

Negative Exponents

Factoring Algebraic Expressions

Combining Like Terms with Exponents

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