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Math Help - Fractional Index Notation Help

  1. #1
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    Fractional Index Notation Help

    Please See the above Picture too see the Question

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  2. #2
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    Re: Fractional Index Notation Help

    Hello, JohnyyMal!

    \text{Prove that: }\:\frac{\sqrt[n]{a^{n+1}}}{\sqrt[n]{a}} \:=\:a

    There are several possible proofs.


    Here is one of them . . .

    \displaystyle \frac{\sqrt[n]{a^{n+1}}}{\sqrt[n]{a}} \;=\; \sqrt[n]{\frac{a^{n+1}}{a}} \;=\; \sqrt[n]{a^n} \;=\;a


    Here is another . . .

    \displaystyle \frac{\sqrt[n]{a^{n+1}}}{\sqrt[n]{a}} \;=\;\frac{a^{\frac{n+1}{n}}}{a^{\frac{1}{n}}} \;=\;a^{\frac{n+1}{n}-\frac{1}{n}} \;=\; a^{\frac{n}{n}} \;=\;a^1 \;=\;a
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