Evaluate each expression in Exercises 55–66, or indicate that the...

Question

Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64

Accepted Answer

Welcome back. I'm so glad you're here. We've got this radical, we have the fifth root of and we've got a fraction. Inside one divided by 1024. Well, we know for previous lessons that this is the same thing as the fifth root of the numerator, divided by the fifth root of the denominator, 1024. And so we can break it apart like this so that we can work on one at a time. We recall that this five here indicates how many of something you need for it to come out. How many of the same factor there has to be for it to come out of the radical. Well, one is really sneaky like this because one can say, well I have five of myself and you say what? How do you do that? And it says well one times one times one times one times one. That's one. So yeah, there's five of me. I want to get out of this radical and the five says, okay, yeah, that checks out. You can come out. And so now we've just got one in our numerator And now let's figure out if there are five of any factors in 1024 and those would get to come out as well. So 1024. Well, we know that's divisible by two, that happens to be two times 512. 512 is also divisible by two, that's two times 256. 256 is also divisible by two. That's two times 128. 128 is also divisible by two. That's two times 64 64 is also divisible by two. That's two times 32. 32 is also divisible by two. That's 2 times 16. 16 is also divisible by two. That's two times 88 is also divisible by two. That's two times four. Are we going to fit four? Is divisible by two. That is two times two. Awesome. So now let's see how many twos do we have? We have 123456789, 10. Well we've got 10 of them but that's the same as two sets of There and 1, 345 here. So this is two to the fifth and this is two to the fifth. So under here. Under this fifth root, we've got two to the fifth, times two to the fifth. And both of these fives are so happy because now they get to come out we've got one divided by Two times two which is the same as one divided by four. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one

Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64

Key Concepts

Radical Expressions

Rational Exponents

Real vs. Complex Numbers

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