1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Confusing answers.

  1. Apr 25, 2004 #1
    I am currently reviewing my whole algebra textbook for a CAT6 test on tuesday. Apparently, it is very difficult, so I'm taking every minute to review.
    Anywho, I ran into 3 problems that are currently driving me crazy. :tongue:

    One concerns roots.
    Here is the problem the book presents:

    My answer was (36x3)1/2. But the book says the answer is (6x)5/2

    BTW, how do you write root signs using the latex program?

    another root problem:


    My answer was x3/4. The book says x11/4 is the answer.

    Now, here is a factoring problem:
    -4(x+16)4 + 9(x+16)2 + x + 16

    On this problem, the part that confuses me is the answer:
    [-4(x+16)3 + 9x + 145) (x+16)

    I arrived at this answer on my own, except I went one step further:
    when I got to [-4(x+16)3 + 9x + 145) (x+16) , I went ahead and rewrote (x+16)3 as (x+16)(x+16)2 so that I could distribute the -4. I then arrived at (x+16)3 (5x+81). Apparently, my final step was incorrect. I would like to know why.

    Also, I did most of these operations in my head (as it is easier for me to do so), so if you would like me to explain anything that I did, I should point out that I may sound unmathematical in a sense.

    Thank you for your time.
  2. jcsd
  3. Apr 25, 2004 #2
    The book is wrong on the first problem, and so are you. ;) Remember the rule that says [tex]a^xa^y = a^{x + y}[/tex]. This rule works even when x or y are fractions.

    [tex](6x^2x)x^{1/2} = (6x^3)x^{1/2} = 6x^3x^{1/2} = 6x^{3 + 1/2} = 6x^{7/2}[/tex]

    For the second problem, remember [tex]\frac{a^x}{a^y} = a^{x - y}[/tex], even when x or y are fractions.

    [tex]\frac{y^3}{y^{1/4}} = y^{3 - 1/4} = y^{11/4}[/tex]
  4. Apr 25, 2004 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    And the last part on factorization. It's just wrong. You cannot pull a factor of x+16 out of the expression again after you've simplified it once. What do you mean to do in "distributing the -4"? You have done something that is against the laws of arithmetic and algebra, that's all.
  5. Apr 25, 2004 #4
    Muzza: Thank you for your kind explanation. It seems to me that from now on, it is far more efficient to calculate roots exponentially; without using a radical.

    Mattgrime: When I said "distribute the -4", I meant applying the distributive property.

    But I see the mistake now. They weren't like terms? (I am referring to the factoring problem)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook