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Express each radical in simplified form. Assume that all variables represent positive real mumbers. See Example 5$$-\sqrt[3]{-216 y^{15} x^{6} z^{3}}$$
Algebra
Chapter 10
Roots, Radicals, and Root Functions
Section 3
Simplifying Radical Expressions
Decimals
Exponents and Polynomials
Equations and Inequalities
Complex Numbers
Campbell University
Harvey Mudd College
Baylor University
Idaho State University
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okay when simplifying this complex. Q Bert here. What we're gonna do is realize that that negative that's a farm stays in front your input, princes around the entire value inside. And then inside, we have the cube root or negative to 16. Now, one thing to notice about that is that it's negative something. They're gonna have a negative value here, right on the route. And the 2 16 is, um, let's think about that is related to any of our known once here. Yeah, it's right here. So we can see that is six. Right? So one cute is one to Cuba's 83 cubes. 27 for Cuba to 64 35 Keep this 1 25 and six. Cute is 216. So six times, six times it. So we know that this is gonna be a negative six. Okay. And then you have your why did the 15th Morgan Day the cube root of wine 15 struck that there's to take the exponents 15 and divided by the root, which is 3 15 divided by three is gonna be fine. Which basically says that if you had why in the fifth Times What if it's time swatting? Fifth, you'd end up with 5 15 francs. That's a perfect cute fruit. And then do the next one, which is gonna be the exit six. What? Six. Divided by 32 So it's gonna be exit the second. Once again, X squared times, export times exported. Next six. And then finally, this last one here is gonna be a three divided by three. Which one? So that means that just Is he right? See, the first is the Thames. Mackenzie is a force. You there. All right, So once we've done simplifying our route, we've got everything here that you're looking at, just trying to make sure we have the right sign on the answer. So is gonna end up being a negative times a negative. So that means this be a positive value at the end is gonna be six white of the fifth X to the second NZ, and that's your simplest form of the Cuban print
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