Perform the indicated operations. Assume all variables represent ...

Question

Perform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 +1)

Accepted Answer

Welcome back. I am so glad you're here. We get to simplify this expression. This is a doozy. We've got in the first set of parentheses. The cubed rut of - the cubed root of and that set of parentheses. Now the new set of parentheses, we have the cube of squared plus the cubed red of times the cubed root of 17 And then plus the cubed root of 11 squared. Alright, so recalling those previous lessons about the order of operations, we are going to do the multiplication inside of the second set of parentheses first So multiplying those two together we get the cubed root of times 17 in there and I'm just going to keep everything as the factors of 11 and 17 until we get to the end. So bringing everything else down we have the cubed root of 17 minus the cubed root Of 11. In the first set of parentheses times the second set of parentheses which has the cubed root of 17 squared plus that. Which we just simplified which is the cubed root of 11 times plus the cubed root of 11 squared. Now we get to distribute that first set of parentheses to everything in the second set of parentheses. So I'm going to start off taking this cubed root of 17 and multiplying it by each term in the second set of parentheses. So the first one here we have the cubed root of 17 times the cubed root of 17 squared. That's going to give us the cubed root Of 17. Cute. There are 3 17 factors in there. Now I'm just going to leave it like that. Now let's take the cubed root of 17 times the second term in the second set of parentheses. The cubed root of 11 times 17. Now that's their positive being multiplied by a positive. So we can have plus and it's still the cubed root. And all of our factors in here are 1 11 and 17. So this is 11 times 17 squared. Alright, now, the last one that this first term gets to get distributed to we have the cubed root of 17 times the cubed root of 11 squared. So that's positive. They're both positive still the cubed root. And are factors on the inside are the squared times the 1 17. Okay, we've distributed that first term. Now let's work on distributing this second term. The negative cubed root of 11 times the first one here, the cubed root of 17 squared. So this will be a minus because we have a positive or negative times a positive and it's still the cubed root. And inside we have an 11 times the 17 squared. Now the next one we have negative cube of 11 times the cube of 11 times 17. So a negative times a positive. This will be minus still the cubed root and we have two elevens. So this will be 11 squared times the 1 17. So 11 squared times 17. Now the last distribution step here, the negative cubed rid of 11 times the positive cubed root of 11 squared negative times a positive is going to be minus. This is still the cubed root. And are factors on the inside are 11 times 11 squared which will be 11 cubed. There are three eleven's there. Okay now the fun part of this one simplifying. Okay this first one here the cubed root of 17 cubed. That's just 17. Woo hoo. Now can we combine any like terms we have got this positive cubed root of 11 times 17 squared. And over here we have this negative cubed root of 11 times 17 squared. They cancel out Yes. Goodbye. Good riddance. We do not want you. We just really don't. Now we have this positive cubed root of 11 squared times 17 and we have this negative cubed root of 11 squared times 17 thing equals 02. Yes. Get out of here we don't want to deal with you. And now this last one here minus the cubed root of 11 cubed. Well that's minus the cubed root of 11 cubed is 11. This whole thing is 17 minus 11. Can you believe it, 17 minus 11 that equals six. So all of that gives us six. We look at our answer choices and that matches with answer choice. A Well done. We'll catch you on the next one

Perform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 +1)

Key Concepts

Cube Roots

Factoring Polynomials

Properties of Exponents

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