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Math Help - Perform indicated operation and simplify

  1. #1
    Junior Member
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    Perform indicated operation and simplify

    (3^4th root of 32a^5) - (a^4th root of 162a)

    How do I go about solving this?

    Oh, BTW, Happy Easter!
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  2. #2
    Super Member

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    Hello, Hapa!

    It's impossible to read what you've typed.
    But I'll take a guess at what you meant . . .


    Simplify: . 3\sqrt[4]{32a^5} - a\sqrt[4]{162a}
    I'll simplify those radicals separately . . .

    . . \sqrt[4]{32a^5} \:=\:\sqrt[4]{16a^4\cdot2a} \:=\:\sqrt[4]{16a^4}\cdot\sqrt[4]{2a} \;=\;2a\sqrt[4]{2a}

    . . \sqrt[4]{162a} \:=\:\sqrt[4]{81\cdot2a} \:=\:\sqrt[4]{81}\sqrt[4]{2a} \:=\:3\sqrt[4]{2a}


    The problem becomes: . 3\left(2a\sqrt[4]{2a}\right) - a\left(3\sqrt[4]{2a}\right)

    . . . . . . . . . . . . . . . = \;6a\sqrt[4]{2a} - 3a\sqrt[4]{2a}

    . . . . . . . . . . . . . . . = \;3a\sqrt[4]{2a}

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