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Math Help - Evaluate Expression

  1. #1
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    Evaluate Expression

    I'm rushing through review homework and I came up against one that I can't solve for the same answer the book has.

    \frac{-5^2\times10+10\times2^4}{-5-3-1}

    The book says this evaluates to 10. I am getting something more like \frac{410}{-9}

    Any ideas what I might be doing wrong? I suspect it's order of operations but I can't nail it.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    re: Evaluate Expression

    Without seeing exactly what you've done it's hard to say where you went wrong.

    \frac{-5^2\cdot10+10\cdot2^4}{-5-3-1}=

    \frac{10\left(2^4-5^2\right)}{-(5+3+1)}=

    \frac{10\left(\left(2^2+5\right)\left(2^2-5\right)\right)}{-(9)}=

    \frac{10(9)(-1)}{(-1)9}=10
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  3. #3
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    re: Evaluate Expression

    Ah, alright, thank you. That makes a lot of sense. I was evaluating each side of the numerator expression first then adding them together (thus the 410). Is this the associative property of mult.?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    re: Evaluate Expression

    Doing that, you would have:

    \frac{-250+160}{-9}=\frac{-90}{-9}=10

    Recall: -5^2\ne(-5)^2...
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  5. #5
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    re: Evaluate Expression

    And again, that also makes a lot of sense, I did not realize that. So the negative is applied after the 5 is squared? Is this always the case without parentheses or is it particular to the leading term of the expression? Apologies, I am returning to math after a 15 year layoff and I've clearly forgotten some details.
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  6. #6
    MHF Contributor MarkFL's Avatar
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    re: Evaluate Expression

    It's an order of operations thing...

    -5^2=-(5^2)=-25

    whereas with (-5)^2 the parentheses causes the negative sign to be applied to the 5 first before squaring, so that we have:

    (-5)(-5)=25
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  7. #7
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    re: Evaluate Expression

    Gotcha. Thanks once more!
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  8. #8
    MHF Contributor MarkFL's Avatar
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    re: Evaluate Expression

    Glad to help!
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