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## Algebra (all content)

### Course: Algebra (all content) > Unit 11

Lesson 8: Radicals (miscellaneous videos)- Simplifying square-root expressions: no variables
- Simplifying square roots of fractions
- Simplifying rational exponent expressions: mixed exponents and radicals
- Simplifying square-root expressions: no variables (advanced)
- Intro to rationalizing the denominator
- Worked example: rationalizing the denominator
- Simplifying radical expressions (addition)
- Simplifying radical expressions (subtraction)
- Simplifying radical expressions: two variables
- Simplifying radical expressions: three variables
- Simplifying hairy expression with fractional exponents

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# Simplifying rational exponent expressions: mixed exponents and radicals

Sal simplifies v^(-6/5)* ⁵√v as v^(-1)..

## Want to join the conversation?

- In the example above , the value of v must be positive, if v equals zero it forms an undefined case .Is it not?!(6 votes)
- Square root of 164(1 vote)

- Why does v have to be greater than or equal to 0 ?(1 vote)
- I left a more detailed answer on the previous video, but in short, taking negative numbers to fractional powers can become messy to deal with, so it's easier to just avoid it when possible.(3 votes)

- Hi. Why v has to be >=0?(2 votes)
- (sqrt(3) - sqrt(6))^2/(sqrt(3) + sqrt(6))(sqrt(3) - sqrt(6))) = (sqrt(3) - sqrt(6))/(sqrt(3) + sqrt(6))(1 vote)
- If v>0 then why are we using the variable V?(1 vote)
- simplifying numbers with rational exponents. What is 32 -3/5 in simplest form?(1 vote)
- You are watching a video about rational exponents. Is part of your problem suppose to be an exponent? Or is this just subtraction of 32 - 3/5 = 31 2/5?

If your problem has an exponent, you need to show that has an exponent, like 32^2 = 32 to the power of 2. Or 4^(1/2) is 4 to the power of 1/2.(1 vote)

- if v is equal to or bigger than 0, then how can it be to the power of negative 1, wouldn't that give us a fraction, which is less than 0 and so not bigger or equal to 0?(1 vote)
- I am unable to find letter k in the skill test so i cant answer the questions ..in fact in all these exponent rational skill tests i cant figure out how to input the anseer even though i know the answer....help(1 vote)
- If you mean that part of the answer is a variable and you can't figure out how to enter the letter, you can just use your keyboard and type the letter. Hope this helps!(1 vote)

- why does v have to be greater than or equal to 0?(1 vote)
- Isn't it impossible to have something to the -1rst power? How does that work. Is -1 also equal to something?(1 vote)
- You can have -1 as an exponent. It indicates to use the reciprocal. For example:

2^(-1) = 1/2

x^(-1) = 1/x

Here is link to videos on negative exponents: https://www.khanacademy.org/math/algebra-home/algebra-basics/core-algebra-exponent-expressions#core-alg-negative-exponents(1 vote)

## Video transcript

- [Voiceover] So I have an
interesting equation here. It says V to the negative six fifths power times the fifth root of V is equal to V to the K power, for V being greater than/equal to zero. And what I wanna do is try to figure out what K needs to be. So what is... what is K going to be equal to? So pause the video and see
if you can figure out K, and I'll give you a hint,
you just have to leverage some of your exponent properties. Alright, let's work this out together. So the first thing I'd want to do is being a little bit consistent in how I write my exponents. So here I've written it as
negative six fifths power, and here I've written it as a fifth root, but we know that the
fifth root of something... we know that the fifth root... the fifth root of V, that's the same way, that's the same thing as saying
V to the one fifth power, and the reason I want
to say that is because then I'm multiplying two
different powers of the same base, two different powers of V. And so we can use our
exponent properties there. So, this is gonna be the same thing as V to the negative six fifths times, instead of saying
the fifth root of V I can say times V to the one fifth power is going to be equal to V to the K. It's gonna be equal to V to the K power. Now, if I'm multiplying V to some power times V to some other power, we know what the exponent
properties would tell us, and I could remind us. I'll do it over here. If I have X to the A times X to the B, that's going to be X
to the A plus B power. So here, I have the same base, V. So this is going to be V to the, and I could just add the exponents. V to the negative six fifths power plus one fifth power, or V to the negative six
fifths plus one fifth power is going to be equal to V to the K. Is equal to V to the K. I think you might see where
this is all going now. So this is going to be equal to V. So negative six fifths plus one fifth is going to be negative
five fifths or negative one. So all of this is going to be equal to negative one, and that's going to be
equal to V to the K. So K must be equal to
negative one, and we're done. K is equal to negative one.