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In $11-38,$ evaluate each expression in the set of real numbers.$$\sqrt[5]{-1}$$

$-1$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 2

Roots and Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $11-38,$ evaluate each …

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Okay, guys. So in this problem, we're given the fifth root of negative one, and we're being asked to simplify this expression and in the problem of states that are expression or simplified answer is gonna be in is gonna be a real number. And so let's start off. So as we've been tackling most of these problems, the first step to do is to rewrite our negative one in a way that our fifth root cancels out with, uh, with the negative ones with the river in form of our negative one. By that, let me explain that the way to get rid of Fifth Root how do you get rid of him through you take the fifth root of something to the fifth power. And in that way we can get rid of the fifth through, and we're just left with that something in the middle. And in order to do the same thing with this problem, we need to rewrite our negative one as naked as something as basically as something So the fifth power. And in order to do that, we're just gonna factor it out. We're gonna see what mould, what? Five things multiplied by itself gives us negative one and thinking about that we get that negative one is actually just native one times itself five times. Now, why is that true? If you just think about it, we know that negative one times negative one is one. No, no, One times negative one is negative. One negative, one times negative One is one and one times negative. One is native simple calculations. And basically, from this, we could basically rewrite fifth root of negative one as the fifth root of negative one to the fifth power and going back to this step right here, the way we cancel out the fifth root is if we have taken the fifth period of something to the fifth Power. We just get that something. This case, we're taking the fifth root of negative one to the fifth power, and as a result, we just getting negative one. So because of these steps, we can literally see that fifth root of negative one is just equal to negative one. Negative one is in the reels. So this satisfies the conditioner problem gave that our expression answer should be in the reels. And just to recap the key step that we made right here is that we connected. Negative one is where we basically made the, uh, algebraic step That negative one is equal to negative one to the fifth power. And that's basically what allowed us to cancel out the fifth root and come down to our final expression. That fifth root of negative one is just equal to you. Negative one. Thank you for listening, guys. And I

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