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. ⁵√(−3)^5

Accepted Answer

Welcome back. I'm so glad you're here. Were given this radical the seventh threat of inside the radical parentheses, negative 18 raised to the seventh and we're supposed to figure out if this is a real number and if so evaluate it. Well, we recall from previous lessons that this seven here tells us how many of the factor there need to be inside of the radical in order for that factor to come out. And inside the radical we have seven negative eighteen's and those seven negative eighteen's line up at the gate and I view this red seven here as a gatekeeper And they say to the gatekeeper, there are seven of us. We want to get out of here and the gatekeeper goes, you're right, there are seven of you. You may come out and they're so excited and they all line up and as they go through that gate of the radical they all merge together now there's just one of them. There's just negative 18 that comes out And that's my very unmask magical explanation and how I remember how to do this process. I'll give you a slightly more mathematical explanation. We know from rules of exponents and radicals that negative raised to the seventh when we have the seventh of that. That's the same as if we had negative 18 to the 7/7 and we can reduce that exponents 7/7. That's one. So we've got negative 18 to the first which is just negative 18. Both of those answers yield negative 18 which matches with answer choice B Well done, we'll catch you on the next one.

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