Make Sense? In Exercises 119–122, determine whether each statemen...

Question

Make Sense? In Exercises 119–122, determine whether each statement makes sense or does not make sense, and explain your reasoning.
____
⁴√(−8)⁴ cannot be positive 8 because the power and the index cancel each other.

Accepted Answer

Welcome back. I am so glad you're here. We're asked to check whether the given statement below is true or false. The statement we're given is that the fourth root of open parentheses, negative six, closed parentheses raised to the fourth power is not equal to positive six. Since the exponent, the exponent is here inside of the radical which this negative six is being raised to and the index, the index is telling us the root of our radical out here will cancel each other. Our answer choices are answer choice. A true and answer choice B false. All right. So do they cancel each other out? They're both fours. It's so tempting to just be like they cancel each other out? It's just negative six. However, we recall from previous lessons that when we're taking the mph rut of a raised to the M power, this is going to equal the absolute value of A when am is even is M E Y M is four, that's even. So the absolute value of A Is the absolute value of -6 Which equals a positive six. So when our statement says that it's not equal to positive six it's wrong. Unfortunately, this statement is false. Our fourth ru of negative six races to the fourth power is equal to positive six. Well done. We'll catch you on the next one.

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Make Sense? In Exercises 119–122, determine whether each statement makes sense or does not make sense, and explain your reasoning. ____ ⁴√(−8)⁴ cannot be positive 8 because the power and the index cancel each other.