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Math Help - need help please!

  1. #1
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    need help please!

    explain the advantage of using rational exponents over the radical sign?
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  2. #2
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    Quote Originally Posted by bobby77
    explain the advantage of using rational exponents over the radical sign?
    I see no advantage. Except it is easier to write.
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  3. #3
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    Hello, bobby77!

    Explain the advantage of using rational exponents over the radical sign?

    Try this problem: . \sqrt{x}\cdot\sqrt[3]{x}


    Since \sqrt[n]{a}\cdot\sqrt[n]{b} \:= \:\sqrt[n]{ab}, the two factors must have the same root.

    We perform some gymnastics: . \begin{array}{cc} \sqrt{x} \:=\:\sqrt[6]{x^3}\\ \sqrt[3]{x} \:= \:\sqrt[6]{x^2}\end{array} . . . did you follow that?

    . . and the problem becomes: . \sqrt[6]{x^3}\cdot\sqrt[6]{x^2} \:=\:\sqrt[6]{x^5}



    With rational exponents: . \sqrt{x}\cdot\sqrt[3]{x}\:=\:x^{\frac{1}{2}}\cdot x^{\frac{1}{3}}\:= \:x^{(\frac{1}{2}+\frac{1}{3})} \:= \:x^{\frac{5}{6}}


    Which way do you prefer?

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