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.
_____
³√x³y¹⁷z²

Accepted Answer

Welcome back. I am so glad you're here. We are asked to simplify the following radical expression by factoring assume that the variables M N and P are positive real numbers. The radical expression we're given is the cubed root of M raised to the 11th power multiplied by N cubed multiplied by P. And our answer choices are answer choice am N cubed multiplied by the cubed red O M squared P answer choice B M cubed N multiplied by the cub of M squared P answer trace C M N cubed multiplied by the cubed root of MP and answer choice D M cubed N multiplied by the cubed A MP. We look at our radical expression and note that the index of our radical is three, meaning that there needs to be three of any factor in order for it to come outside of the radical. And we can take a look at our three variables on the inside and expand some of them in order that they can come in groups of three for their factors. So for example, taking M rays to the 11th power, we can expand that to be M cubed multiplied by M cubed multiplied by M cubed multiplied by M squared. Because we recall from previous lessons that when we have like bases, those are the MS being multiplied, we can add their exponents together and three plus three plus three plus two equals 11. And taking a look at these M cubes, there are three of them. So that's M cubed cubed. So there are three of the factor M cubed that is still multiplied by M squared. But we could expand our radical. We still have the cubed root of. But now we can write that as M cubed cute multiplied by M squared instead of M rays to the 11th power. Now N cubed that's already coming in three for that factor. So we can continue with multiplied by N cubed and that's still multiplied by P. We can't expand P any further. But we do now have the ability to take out this M cubed and the N cubed. And when they come out, they lose their cube. So we'll just have on the outside of the radical, we'll have M cubed N and that's still multiplied by the cubed of and left on the inside will be M squared P. And we look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

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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. _____ ³√x³y¹⁷z²