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Math Help - rational exponents? Solve please

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    rational exponents? Solve please

    (-3a1/4)(9a)-3/2
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    Re: rational exponents? Solve please

    Quote Originally Posted by zbest1966 View Post
    (-3a1/4)(9a)-3/2
    Here are some properties you should know:

    a^ma^n = a^{m+n}

    (ab)^n = a^nb^n

    a^{m/n} = \sqrt[n]{a^m}
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    Re: rational exponents? Solve please

    I understand the properties but how do you solve it.
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    Re: rational exponents? Solve please

    Quote Originally Posted by zbest1966 View Post
    I understand the properties but how do you solve it.
    If you understood the properties, I suspect you would not be having difficulties with the problem. By the way, we have nothing to "solve" here, this is not an equation. Rather, we are "simplifying" the expression.

    \left(-3a^{1/4}\right)(9a)^{-3/2}

    =-3a^{1/4}\cdot9^{-3/2}a^{-3/2}

    =-\frac{3a^{1/4}}{9^{3/2}a^{3/2}}

    =-\frac{3a^{1/4}}{27a^{3/2}}

    Now, use the properties \frac{a^m}{a^n} = a^{m-n} and a^{-n} = \frac1{a^n} to finish it:

    =-\frac{a^{-5/4}}{9}=-\frac1{9a^{5/4}}

    As a final step, you may want to convert a^{5/4} to radical form, depending on the problem's instructions.
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    Re: rational exponents? Solve please

    Quote Originally Posted by zbest1966 View Post
    I understand the properties but how do you solve it.
    You could actually apply the properties you say you understand or you could ask someone else to solve it for you. I see you chose the second solution method.
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