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Express each radical in simplified form. Assume that all variables represent positive real mumbers. See Example 5$$-\sqrt[4]{162 r^{15} s^{10}}$$
$-3 r^{3} s^{2} \sqrt[4]{2 r^{3} s^{2}}$
Algebra
Chapter 10
Roots, Radicals, and Root Functions
Section 3
Simplifying Radical Expressions
Decimals
Exponents and Polynomials
Equations and Inequalities
Complex Numbers
Missouri State University
Campbell University
Oregon State University
Harvey Mudd College
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In mathematics, the absolu…
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Express each radical in si…
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give her this whole action when we're working with the fourth were here, So I have weakness for spares and queues. I don't really do this with four through. If he did x to the fourth and be one of the fourth is one times 11 which is one to the fourth me two times, Two times, two times two. Which is gonna leave 16 three of the fourth of you three times, three times, three times three, which is gonna be 81. And you got the idea. I don't think really need much more than that for this problem. So if we're looking at the exponents next the fourth, it would be one to the fourth to the fourth and three of the fourth. As you see it above here, once we have the understanding, we can see that 1/16 isn't that we can work with. So let's take a look at this. This is gonna be the same as before, through of with value of 1 16 and then times the four through of are under the age times, the four through of to the 20th. Okay. And so this is really easy to work with right before through part of the A that's gonna be just eight divided by four, which is too. So this we are the second as artists like intends on the second times are the second time's Our second is, of course, our A And then here we have 25 by forces us to be, uh, an expert of five on the tea because tea the fifth times to you that that time to teach that time. See the feathers, Of course you. But the 1st 1 here is a fraction. And remember, you can apply that route to the top in the bottom of the fraction, so we simplify it. This is the same as the fourth root of one over the fourth root of 16. Okay, now, the fourth out of one is a known value for three of one is, of course, one of the 43 or 16 is unknown value. It's of course, too. So, really, what we have here is the fourth through of 1/16. It's just one that is 1/2 1 half times one raft. That's what half is 1 16 So our final answer is just gonna be 1/2 aren't of the second See to the fifth, and you are
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