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Math Help - Bah! I am lost with exponents!

  1. #1
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    Bah! I am lost with exponents!

     \sqrt[4]{16a^7b^8} = 2ab^2 \sqrt[4]{a^3}<br />

    I don't know how to make the jump from the first thing to the last thing.

    EDIT: There was a typo, sorry.
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  2. #2
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     <br />
\sqrt[4]{16a^7b^8}<br />

    =\sqrt[4]{16a^3a^4b^8}

    =\sqrt[4]{16}\sqrt[4]{a^3}\sqrt[4]{a^4}\sqrt[4]{b^8}

    =2ab^2\sqrt[4]{a^3}

    Does this help?
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  3. #3
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    Quote Originally Posted by Kasper View Post
     <br />
\sqrt[4]{16a^7b^8}<br />

    =\sqrt[4]{16a^3a^4b^8}

    =\sqrt[4]{16}\sqrt[4]{a^3}\sqrt[4]{a^4}\sqrt[4]{b^8}

    =2ab^2\sqrt[4]{a^3}

    Does this help?
    I dont mean to intrude, but would someone mind expanding on this solution? Im not sure I quite understand the fine details of what is going on here.

    Thanks
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  4. #4
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    Quote Originally Posted by allyourbass2212 View Post
    I dont mean to intrude, but would someone mind expanding on this solution? Im not sure I quite understand the fine details of what is going on here.

    Thanks
    For sure!

    Well because a^3a^4=a^7 Just a small expansion.

    <br />
\sqrt[4]{16a^3a^4b^8}<br />

    By the rule \sqrt{ab}=\sqrt{a}\sqrt{b}, so we can split up the expression and take the fourth root of each term.

    For additional clarification, I will rewrite that.

    <br />
\sqrt[4]{16}\sqrt[4]{a^3}\sqrt[4]{a^4}\sqrt[4]{b^8}<br />
<br />
=\sqrt[4]{2^4}\sqrt[4]{a^3}\sqrt[4]{a^4}\sqrt[4]{b^8}<br />
=2ab^2\sqrt[4]{a^3}

    Does this help, or should I clarify more?
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