In Exercises 29–44, simplify using the quotient rule.
_____
³√11/...

Question

In Exercises 29–44, simplify using the quotient rule.
_____
³√11/64

Accepted Answer

Welcome back. I am so glad you're here. We're asked to use the quotient rule for the simplification of the cubed root of the fraction in the numerator. We have 69 and that's divided by 512. Our answer choices are answer choice. A the cubed root of 23 Divided by eight answer choice B three multiplied by the cubed dr of 23 Divided by eight answer choice C The Cub dr of divided by eight in the answer choice D the negative Cubed Threatt of 69 divided by eight. All right, we recall from previous lessons that the quotient rule tells us that when we're taking the root of a fraction, we can rewrite that, taking that same rot. So in this case, the cub dr of both the numerator and the denominator. So in this case, we've got the cubed rot of the numerator 69 divided by the cubed rut of the denominator 512. Now we can work to simplify our numerator and then our denominator When simplifying radicals, we first look at our index and our index here is three that tells us that we need three of any factor in order for it to come outside of the radical. So let's first look at 69, 69 is three multiplied by 23. But that's as simplified as it gets. And there aren't three of any factor. There's a three, but there aren't three of any factor. So we can't actually simplify that one. We can't take anything out of that cubed rut of 69. So our numerator remains the cubed rut of 69. That's divided by now, let's take a look at our denominator 512, 512 is going to be eight multiplied by 64, is eight multiplied by eight. So in this case, we've got eight multiplied by eight multiplied by eight or in other words, eight cubed. So in our denominator, we could rewrite that as the cubed root of eight cubed. And when we're taking the cubed rot of anything cubed, the thing being cubed, the factor in this case, the eight gets to come outside of the radical. So rewriting this, our numerator remains the same. The cubed threat of 69 and the denominator, this is divided by the cubed threat of eight cubed which simplifies to just eight. So this is as simplified as this one 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 29–44, simplify using the quotient rule. _____ ³√11/64

Key Concepts

Quotient Rule

Radical Expressions

Simplifying Fractions

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