# Math Help - Fractional Index Notation Help

1. ## Fractional Index Notation Help

Please See the above Picture too see the Question

Many Thanks

2. ## 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 . . .

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