In Exercises 77–90, simplify each expression. Include absolute va...

Question

In Exercises 77–90, simplify each expression. Include absolute value bars where necessary.
____
³√−8x³

Accepted Answer

Welcome back. I am so glad you're here. We are asked to rewrite the following algebraic expression. In the simplest form possible use absolute value bars if needed. The algebraic expression we're given is the cubed rut of open parentheses, negative 125 P cubed closed parentheses. Our answer choices are answer choice, a -125 p answer choice B The absolute value of 25 p answer choice C negative five P and answer choice D, the absolute value of P divided by five. All right. So when we're simplifying radical expressions, we first want to look and see what the index of our radical is. The index here for this one is three. That means we need three of any factor in order for it to come out of the radical. And we also notice that here inside of our radical, we've got a negative, We have a negative 125 p cubed, we can take the root of a negative when our index is odd. And in this case, our index is odd three is odd. So we can proceeded. So we ask ourselves, can we take the cubed root of negative 125. Or in other words, is there anything that multiplied by itself three times equals negative 125. And yeah, negative 125 is negative five cubed. So we can rewrite this underneath the radical. We have the cubed root of instead of negative 125 we can say negative five inside of parentheses cubed. And now this P cubed, well, that is already cubed. There are three ps here, this is great. Now anything that is cubed gets to come outside of the cubed rut, so we'll be taking out a negative five and A P. Both of those are cubed when they come outside of the radical, they lose their cubed. So coming out is just going to be negative five P and that's it, that is our expression simplified. That's as simplified as it gets. We look at our answer choices and this matches with answer choice. See, well done. We'll catch you on the next one.

In Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√−8x³

Key Concepts

Cube Root

Negative Numbers and Odd Roots

Absolute Value

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