In Exercises 39–60, simplify by factoring. Assume that all variab...

Question

In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers.
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Accepted Answer

Welcome back. I am so glad you're here. We are asked to simplify the following radical expression by factoring assuming that B is greater than zero, our radical expression is the fifth threat of B raised to the 13th power. Our answer choices are answer choice A B squared multiplied by the fifth of be raised to the fourth power. Answer choice BB squared multiplied by the sister of be cubed answer trace CB cubed multiplied by the fifth Ave B squared and answer trace DB cubed multiplied by the fifth rate of be cubed. All right. The first thing we do in simplifying radicals is we look at our index to see what that is. And in this case, it's five that tells us that we need five of any factor in order for it to come outside of the radical. So right now we've got 13 bees and there are several ways to figure out how many can come out of the radical. I'll show you a couple. So first you could write out 13 BS multiplied together. B multiplied by B 13 times. There's three, six, nine, 10 or 12 and 13. And so they need to come in groups of five in order to get out. So we can figure out groups of five. Here's the first five, here's another group of five and then there's only three left over. So essentially, we have two groups of be raised to the fifth power. So we have be raised to the fifth power squared and that's still multiplied by this B raised to the third power. And so something has to be raised to the fifth power. In order for it to come out, essentially, we're going to get two of these be raised to the fifth powers to come out. That's how many of them, there are, two of them will get to come out. So when they come out of the radical, they lose their fifth power. So if we have the fifth threat of B race to the 13th, then it's going to lose that fifth power. All that's left are just two BS that get to come out. So we'll have B squared left on the outside and that B raise to the third power is still on the inside. So it's still being multiplied by the fifth threat of B cubed. Now, there are other ways to do this other than writing out 13 bees, you can take this 13 on the inside of the ex the exponent. There, we have 13 and you can divide that by 5, 13, divided by five is going to get you two with a remainder of three. And so that's where, you know, you're going to have two of them. And what you could do is you could group them instead into twos. So you can take these, group them into twos. And you know that way you have B squared five times and that's still multiplied by that B cubed. But again, here you've got something raised to the fifth power. So the B squared is what's going to come out of the radical and be in front. And that B cubed is what's left inside because there aren't five of that factor. So that is how you factor this one. And we look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. ___ ⁵√y¹⁸

Key Concepts

Radicals

Exponent Rules

Factoring

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