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In $11-38,$ evaluate each expression in the set of real numbers.$$\sqrt[k]{x^{2 k}}, k \text { an integer greater than } 2$$

$z^{2}$

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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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okay. Hey, guys. So in this problem, we're given a slightly different variation of the simplification of radical. We were given the Kate the root of X to the two k power. And we're told that our kay is greater than two and that our kay is an element of the interviews. Basically, K's an integer, and this symbology right here is basically saying that Kay's an integer z Z represents the set off. Oh, set of all integers just Cem mathematical terminology for you guys and show our goal is to simplify his expression, find a real value answer. The assumption is that X is also a real number. We're not assume that exes around core irrational like the basic assumption is that X is a real number. R two R k is an integer, and that is greater than two. So our first step is to try to rewrite this radical. So we get the kid root of something to the cape our cause. That's how we get rid of our radicals. When you take the K through of something to the cape. Our you're just left with that thumping. So let's try to do that. So we have the K through of X to the two K. Now, if you remember your exponents, rules are exploding. Rules state that if you have X to the A being power, that's equal to X to the A all to the B power or X to the B all to the A power. Now our extra, The two K is off the form X a b so we could rewrite our extra the two K, as in any of these two forms and the form that we want is we want our K to be on the outside of our parentheses. We want our K to be the outermost exponents. So it cancels out with our Kate fruit. So what we're gonna do is we're gonna rewrite this expression as the Kate, the root of X squared to the K power. And in doing so, we have the Kate route off something to the K power and that just gives us or something. And that is that it gives us X square. So the answer to this problem is X squared. I hope this made sense, guys. And just to highlight the key step that we made it the key step that we made is recognizing this exponents rule trick. Not really a trick. It's one of the rules of exponents simplifying exponents. The power room important is step in simplifying or extra to Cato X squared to the Cape power. And that's what gave us our X squared. So thanks for listening, guys. And I hope this, huh?

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