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Math Help - Exponent confusion.

  1. #1
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    Exponent confusion.

    Um. i was out the day of the lesson for this assignment, and i read the book's lesson, but it doesn't explain everything. Basically, it says
    a^3  a^2 = a  a  a  a  a = a^5
    so i learn that a^3 a^2 (in this situation) is basically adding the exponents. no problem.
    then it says...
    (3^5)^2 = 3 to the power of 10
    ok, so you multiply parethetical exponents and outside exponents. again, nothing difficult.
    then it says..
    (6  5)^2 = 6^2  5^2 = 36  25 = 900
    add the exponent to everything in parenthesis. again, easy.
    but then you get to the problems...
    (3b)^3  b
    um. so like, you have 3b^3, and multiply it by 1b? so it's... still 3b^3? or did i mess up somewhere?
    5^3  (5a^4)^2
    5^3=125, so it's 125 ...5a^8? or 5a^6? @_@
    4x  (x  x^3)^2
    buhhh.... 4x (x^4)^2.. 4x x^8... 4x^8?

    there's more confusing ones, but hopefully i can sort most of them out if i get these figured out...thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Forkmaster View Post
    then it says..
    (6  5)^2 = 6^2  5^2 = 36  25 = 900
    um, that's wrong, unless you have a typo. as in, you meant to write (6 \cdot 5)^2

    use the command \cdot to put the multiplication dot in... you can't post images in LaTeX and expect them to work.

    (3b)^3  b
    um. so like, you have 3b^3, and multiply it by 1b? so it's... still 3b^3? or did i mess up somewhere?
    do one piece at a time.

    so we have (3b)^3b

    work out the cubed part first, we get:

    (3^3 b^3)b = (27b^3)b

    now multiply the b's, using the first rule you posted

    you get: 27b^4

    now try the others
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  3. #3
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    Quote Originally Posted by Forkmaster View Post
    Um. i was out the day of the lesson for this assignment, and i read the book's lesson, but it doesn't explain everything. Basically, it says
    a^3  a^2 = a  a  a  a  a = a^5
    so i learn that a^3 a^2 (in this situation) is basically adding the exponents. no problem.
    then it says...
    (3^5)^2 = 3 to the power of 10
    ok, so you multiply parethetical exponents and outside exponents. again, nothing difficult.
    then it says..
    (6  5)^2 = 6^2  5^2 = 36  25 = 900
    add the exponent to everything in parenthesis. again, easy.
    but then you get to the problems...
    (3b)^3  b
    um. so like, you have 3b^3, and multiply it by 1b? so it's... still 3b^3? or did i mess up somewhere?
    5^3  (5a^4)^2
    5^3=125, so it's 125 ...5a^8? or 5a^6? @_@
    4x  (x  x^3)^2
    buhhh.... 4x (x^4)^2.. 4x x^8... 4x^8?

    there's more confusing ones, but hopefully i can sort most of them out if i get these figured out...thanks
    These exponent rules are merely a way of counting factors. Count the number of factors of a in the following "laws" in order to get the rules.
    a^m = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{m times} \end{array}

    a^m \cdot a^n = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{m times} \end{array} \cdot \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{n times} \end{array} = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{m + n times} \end{array} = a^{m + n}

    (a^m)^n = \begin{array}{c} \underbrace{a^m \cdot ~ ... ~ \cdot a^m} \\ \text{n times} \end{array} = \begin{array}{c} \underbrace{(a \cdot a \cdot ~ .... ~ \cdot a)} \\ \text{mn times} \end{array} = a^{mn}

    (ab)^m = a^mb^m
    (You can sketch that one out yourself.)

    So let's take apart one of your problems.
    (3b)^3 \cdot b

    = (3^3b^3)b = 3^3 \cdot b^3 \cdot b

    = 27(b^3 \cdot b^1) = 27b^{3 + 1} = 27b^4

    Always do the parenthesis first.

    -Dan
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  4. #4
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    For (3b)^3  b:

    You can split it into  (3^3)  (b^3) (b^1) Remember that 3 and b are separate terms in parenthesis, you need to cube both of them.

    For 5^3  (5a^4)^2:

    Again, 5 and  a^4 are separate terms, so you need to square both of them, giving you:

     (5^3)(5^2)(a^8)
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    um, that's wrong, unless you have a typo. as in, you meant to write (6 \cdot 5)^2
    yes, i meant to do the math dot. im new to the LaTex thing :P.

    thanks for the quick replies. i think i got it now, figured out a few on my own..here's hoping that there's no suckerpunch ones that have entirely new content like this book tends to do, lol
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  6. #6
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    Found another one that confused me a bit, but only in one place.
    (-ab)(a^2b)^2
    distribute the ^2 in the second parenthesis...
    (-ab)(a^4b^2)
    now multiply them together...
    the b becomes b^3, but what of the a?
    -a a^4...
    would it be a^3? -a^4? a to the power of -4? i'm confused.
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Forkmaster View Post
    Found another one that confused me a bit, but only in one place.
    (-ab)(a^2b)^2
    distribute the ^2 in the second parenthesis...
    (-ab)(a^4b^2)
    now multiply them together...
    the b becomes b^3, but what of the a?
    -a a^4...
    would it be a^3? -a^4? a to the power of -4? i'm confused.
    you can think of -a \cdot a^4 as -1 \cdot a \cdot a^4

    so now, just multiply the a's as normal, and then apply the minus 1
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  8. #8
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    Got it. Thanks.
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