Sweetpeach Posted October 17, 2011 Share Posted October 17, 2011 Hi Hivers, This afternoon, my son is working along on the Alcumus portion of AofPS and we come up against a question that stumps him. [(x^3/2x)^x/9 * (x^9/15)^5/18]^3 He could simplify the right hand side of the * sign, but couldn't get there with the x variable in the first expression. The tricky slice for me, the non-mathy mother, is I couldn't even find an online example for working it out. I guess the goal of Alcumus is to stretch the student into applying what he knows (?) but I find it uber-frustrating because I don't know what specific rule we're missing and I don't know how to find out what it is we're missing. Do you have "go-to" resources that you use when you're stumped? We use Khan Academy but often, I don't know the proper name for the skill that needs application. It's like looking for a needle in a haystack. Anyone have thoughts about this? Warmly, Tricia Quote Link to comment Share on other sites More sharing options...
kiana Posted October 17, 2011 Share Posted October 17, 2011 Whoaaa ... did you enter that right? Because I put it into wolfram alpha and it was *horrible*. http://www.wolframalpha.com/input/?i=%5B%28x%5E3%2F2x%29%5Ex%2F9+*+%28x%5E9%2F15%29%5E5%2F18%5D%5E3 Quote Link to comment Share on other sites More sharing options...
regentrude Posted October 17, 2011 Share Posted October 17, 2011 (edited) I would try the AoPS boards for help. Are you sure you have copied the expression correctly? ETA: The only concepts involved here are laws of exponents: (x^a)^b=x^(a*b) and (x^a)*(x^b)=x^(a+b) Edited October 17, 2011 by regentrude Quote Link to comment Share on other sites More sharing options...
Dana Posted October 17, 2011 Share Posted October 17, 2011 Not looking at your specific example, but you're likely looking for exponential rules (or writing radicals in exponential form, & then using exponential rules). Khan Academy is good & so is PurpleMath (purplemath.com). Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted October 17, 2011 Author Share Posted October 17, 2011 Whoaaa ... did you enter that right? Because I put it into wolfram alpha and it was *horrible*. http://www.wolframalpha.com/input/?i=%5B%28x%5E3%2F2x%29%5Ex%2F9+*+%28x%5E9%2F15%29%5E5%2F18%5D%5E3 :) Simplify. Not calculate. And we use the AofPS boards regularly. They are probably tired of us. The other piece of this problem is I need to figure out a way to get ds organized, writing down solutions from Alcumus, taking care of his notes etc etc. Otherwise, we all might go down on this ship. I like this class set-up and think AofPS is brilliant. I just need to get my head wrapped around it. Which means my goal of me being "laissez-faire" with Matt's math might not come to fruition anytime soon. Tricia Quote Link to comment Share on other sites More sharing options...
kiana Posted October 17, 2011 Share Posted October 17, 2011 :)Simplify. Not calculate. And we use the AofPS boards regularly. They are probably tired of us. The other piece of this problem is I need to figure out a way to get ds organized, writing down solutions from Alcumus, taking care of his notes etc etc. Otherwise, we all might go down on this ship. I like this class set-up and think AofPS is brilliant. I just need to get my head wrapped around it. Which means my goal of me being "laissez-faire" with Matt's math might not come to fruition anytime soon. Tricia That *was* the simplification -- what you wrote simplifies to (2^(-3-3 x) x^135 (x^2)^(3 x))/232714766997894287109375, which is why I thought you might've entered it wrong. Quote Link to comment Share on other sites More sharing options...
regentrude Posted October 17, 2011 Share Posted October 17, 2011 That *was* the simplification -- what you wrote simplifies to (2^(-3-3 x) x^135 (x^2)^(3 x))/232714766997894287109375, which is why I thought you might've entered it wrong. I think she means the fractions to be in the exponents - that would be more in line with what I would guess the purpose of the problem to be, at least in the second factor. Sweetpeach: are 3/2x and 9/15 and 5/18 the exponents??? Then (x^(3/2x))^(x/9) = x^ ((3/2x *x/9))= x^(1/6) (x^9/15)^5/18]^3= x^((9/15)*(5/18)*3)=x^(1/2) and [(x^3/2x)^x/9 * (x^9/15)^5/18]^3 = x^(1/6)*x^(1/2)= x^(1/6+1/2)=x^(2/3) I would be inclined to believe this is much more likely to be the correct problem. If so, Sweetpeach, you need to be clearer with your notation and use parentheses. Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted October 17, 2011 Author Share Posted October 17, 2011 If so, Sweetpeach, you need to be clearer with your notation and use parentheses. Hey there, Regentrude, thanks for that encouragement. :tongue_smilie: I clearly feel way over my head with this and I was looking for some support as I try to navigate this. It's been tricky. Maybe I'll try again later to post the question, with the appropriately placed exponents and brackets. Cheers, Tricia Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted October 17, 2011 Author Share Posted October 17, 2011 (edited) & Edited October 17, 2011 by Sweetpeach Quote Link to comment Share on other sites More sharing options...
regentrude Posted October 17, 2011 Share Posted October 17, 2011 That's too bad that you don't want to come back- I would like to know what the instructor said. What's the solution? ARE the fractions the exponents, or not? Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted October 17, 2011 Author Share Posted October 17, 2011 Argh. See, I could just cry my head off and I'm fragile when it comes to math. I can't even write it down correctly. sigh. It is: ((x^3/2x)*x/9 * (x^9/15)* 5/18)^3 The alcumus font is little and we thought it was to the power of x/9 and to the power of 5/18 and even in my pea-sized math brain, that seemed crazy?!?!?! The instructor has helped us. In spite of me, I hope my kids get a decent math education. Cheers, Tricia Quote Link to comment Share on other sites More sharing options...
regentrude Posted October 17, 2011 Share Posted October 17, 2011 I am glad you got the instructor's help. Don't beat yourself up, stuff like this can happen easily, especially if the font is very small. And please don't hesitate to keep coming here for help :) Argh. See, I could just cry my head off and I'm fragile when it comes to math. I can't even write it down correctly. sigh. It is: ((x^3/2x)*x/9 * (x^9/15)* 5/18)^3 The alcumus font is little and we thought it was to the power of x/9 and to the power of 5/18 and even in my pea-sized math brain, that seemed crazy?!?!?! The instructor has helped us. In spite of me, I hope my kids get a decent math education. Cheers, Tricia Quote Link to comment Share on other sites More sharing options...
LidiyaDawn Posted October 17, 2011 Share Posted October 17, 2011 [(x^3/2x)^x/9 * (x^9/15)^5/18]^3 That looks like what happens when my cat wanders across my keyboard. :w00t: Quote Link to comment Share on other sites More sharing options...
kiana Posted October 17, 2011 Share Posted October 17, 2011 Argh. See, I could just cry my head off and I'm fragile when it comes to math. I can't even write it down correctly. sigh. It is: ((x^3/2x)*x/9 * (x^9/15)* 5/18)^3 The alcumus font is little and we thought it was to the power of x/9 and to the power of 5/18 and even in my pea-sized math brain, that seemed crazy?!?!?! The instructor has helped us. In spite of me, I hope my kids get a decent math education. Cheers, Tricia Hey Sweetpeach, I am sorry if I hurt your feelings. The problem seemed totally 100% crazy to me as well, so I assumed there must have been a typo somewhere because it was toooooo crazy. :( Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted October 18, 2011 Share Posted October 18, 2011 (edited) Argh. See, I could just cry my head off and I'm fragile when it comes to math. I can't even write it down correctly. sigh. It is: ((x^3/2x)*x/9 * (x^9/15)* 5/18)^3 Are you SURE about this correction? Because the expression as you typed it originally simplified down to just plain x, which is the way I would expect an Alcumus problem to behave. This one is much nastier! Let me explain the original expression, one piece at a time: [(x^3/2x)^x/9 * (x^9/15)^5/18]^3 You have to use the order of operations: Work on the stuff inside the square brackets first, and simplify the exponents before you try to mess with the multiplication. The first piece is (x^3/2x)^x/9, which uses the exponent rule that (x^a)^b = x^(ab). The two fractions are exponents, and because you have a power raised to another power, the exponents get multiplied. And then, of course, you have to put the resulting fraction into lowest terms: (3/2x)(x/9) = (3x/18x) = 1/6. Therefore, this first messy piece simplifies to x^(1/6). The second piece is (x^9/15)^5/18, which uses the same exponent rule. Power raised to another power, so the exponents again get multiplied. This also simplifies to x^(1/6). The third piece is the product inside the square brackets, which is now x^(1/6) * x^(1/6). It uses the rule x^a * x^b = x^(a+b), and simplifies to x^(1/3). Finally, we apply the cube that is outside the square brackets, which simplifies our final answer to just plain x. Edited October 18, 2011 by letsplaymath typo with my cut-and-paste. Aargh! and adding a few extra lines of explanations. Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted October 18, 2011 Share Posted October 18, 2011 On the other hand, the new expression doesn't simplify nicely at all: ((x^3/2x)*x/9 * (x^9/15)* 5/18)^3 = {(5/162) * x^[(3/2x) + 1 + (9/15)]}^3 = (125/4,251,528) x^[(144x + 135)/30x] That is the simplest I can figure out how to make it look. In my experience, Alcumus isn't that mean! Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted October 18, 2011 Author Share Posted October 18, 2011 Hi Denise, thank you for weighing in on these matters. There are some slices of my life where I can stand up for myself but math isn't one of those slices. I went back and looked again at the above explanations, looked at the simplification given to us by the instructor, looked again at the alcumus question. Quite frankly, I can't really tell whether the x/9 and the 5/18 is * or ^? I wish I could find a "mathy mom" in the class who might come alongside me . . . I'll inbox you later on today. Warmly, Tricia Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted October 18, 2011 Author Share Posted October 18, 2011 Hey Sweetpeach, I am sorry if I hurt your feelings. The problem seemed totally 100% crazy to me as well, so I assumed there must have been a typo somewhere because it was toooooo crazy. :( Hey, I forgive you. It's all good. These interactions have reminded me that everyone has strengths and weaknesses and to be extra kind in all circumstances . . . people have all sorts of real struggles and it's good for me to have lots of grace for those that might struggle in my areas of strength or accomplishment in that same way that I need grace for my weaknesses. Math is a mountain I'd like to climb but it's a steady uphill battle. Warmly, Tricia Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted October 18, 2011 Share Posted October 18, 2011 Whenever you need an alternate explanation to help you understand something in algebra, Purplemath is a great place to start. Here is their page on exponent rules. And then just remember: All exponents follow the same rules, even if they are fractions. And multiplying or adding or doing anything with fractions will work the same way it always does, even if the fractions are exponents. As for this problem, since even the instructor found it hard to interpret, I would forget about it and focus on whatever comes next. And if you run into trouble again, feel free to ask a new question. I'm sure any of us "mathy moms" would be glad to help! Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted October 18, 2011 Author Share Posted October 18, 2011 Hi Denise, I can't thank you enough. Truly. You are certainly a Woman of Grace. I have a feeling that we'll be stretched in both ways over the next few months --- AofPS is pulling us forward and we'll need to walk backwards a bit to fill in some gaps. Looks like I'm going on a math adventure! Thank you for the links. Warmly, Tricia Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted October 20, 2011 Share Posted October 20, 2011 I shared this problem on my blog, and a friend reminded me of something I forgot to say: Because x is in the denominator of one of the exponents, we have to note in our answer that it can't equal zero. Quote Link to comment Share on other sites More sharing options...
Sweetpeach Posted November 16, 2011 Author Share Posted November 16, 2011 Denise, love the visual! Thank you! I'm pleased to report that our AofPS journey is much smoother . . . we've got the system figured out. Before the class: Do all of the discovery-based problems. Read the textbook and figure it out as best you can. Do the class with the fabulous prof! After class, 1) do the teacher questions online 2) do the review problems at the end of the chapter. Try the challenge problems. 3) hang out with Alcumus and stay on top of those questions. Weekend work . . . do the discovery-based problems for the next chapter. It took a month of feeling crazy, but all is now well at our home when it comes to math learning. For sure, my ds2 is doing Pre-Alg 1 & 2 with AofPS. By the time dd3 comes along, I'll be a mathy mama! :) Now, Geeknick, good luck with your post! *I can't help you.* (mildly understated). Warmly, Tricia Quote Link to comment Share on other sites More sharing options...
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