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Math Help - Exponents Expressed As Roots

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    Exponents Expressed As Roots

    With an exponent you can express it as a .....

    Original Exponent: 7(5)^\frac{1}{2}
    =17.5

    Express it as a fraction: \frac{7}{5^\frac{-1}{2}}}
    =17.5

    Express it as a root: 7\sqrt{5}
    plugging the above into a calculator yields 15.65. Did I do something incorrect, shouldn't it equal 17.5 like the other examples? Am I doing something incorrectly? Thanks
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    Re: Exponents Expressed As Roots

    Quote Originally Posted by allyourbass2212 View Post
    Express it as a root: 7\sqrt{5}
    plugging the above into a calculator yields 15.65. Did I do something incorrect, shouldn't it equal 17.5 like the other examples? Am I doing something incorrectly? Thanks
    Yes, I think you are not using your parentheses correctly in the first two expressions.

    7\cdot5^{1/2} = \frac7{5^{-1/2}} = 7\sqrt5\approx15.652.

    What you were probably calculating was

    7\cdot\frac{5^1}2 = 17.5,

    which is how your calculator would interpret 7*5^1/2 if you don't put parentheses around the exponent (remember that exponents have higher precedence than division in the order of operations).
    Thanks from allyourbass2212
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