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Math Help - I need help simplifying this expression...

  1. #1
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    I need help simplifying this expression...

    Could somebody please explain how to simplify this expression?
    (x1/4*y5/2)^-2
    Write your answer without using negative exponents.
    Assume that all variables are positive real numbers.


    Thank you in advance.
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  2. #2
    Senior Member topher0805's Avatar
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    Just to clarify, is this your expression?

    (x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2}
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  3. #3
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    Yes, that's correct.
    Sorry, forgot the ^'s before the fractions.
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  4. #4
    Senior Member topher0805's Avatar
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    <br />
(x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2}<br />

    Recall that when you raise a variable to a negative exponent like this:

    <br />
x^{-2}

    You can change the sign of the exponent by dividing the variable into 1. So:

    <br />
x^{-2} = \frac {1}{x^2}

    Using this rule, we can say that:

    <br />
(x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2} = \frac {1}{(x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{2}}<br />

    Recall the rule of exponents that says:

    <br />
(x^a)^b = x^{ab}

    So we can simplify our expression to:

    \frac {1}{(x^{\frac {2}{4}}\cdot y^{\frac {10}{2}})}

    Simplify the fractions:

    \frac {1}{(x^{\frac {1}{2}}\cdot y^5)}

    And recall that x^{\frac {1}{2}} = \sqrt {x}

    So your final expression is:

    \frac {1}{\sqrt {x}\cdot y^5}
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  5. #5
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    Oh wow, thank you so much.
    I'll record that into my notes!
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