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Thread: 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:

    $\displaystyle a^ma^n = a^{m+n}$

    $\displaystyle (ab)^n = a^nb^n$

    $\displaystyle a^{m/n} = \sqrt[n]{a^m}$
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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.

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

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

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

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

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

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

    As a final step, you may want to convert $\displaystyle a^{5/4}$ 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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