Tuesday 23 August 2016

Simplifying exponential fraction



I have this exponential fraction
$$\frac{2^{n+1}}{5^{n-1}}$$



I was wondering how we simplify something like this.




I know if the top and bottom had the same like $\frac{2^{n+1}}{2^{n+1}}$, you would just subtract the exponent.



But in my situation, I'm not too sure how to tackle it.


Answer



$\frac{2^{n+1}}{5^{n-1}}=2\times 5\times \frac{2^n}{5^n}=10\times \left(\frac{2}{5}\right)^n=10\times 0.4^n$ if you wish. But if you are dealing with simplifying fractions, I do think your answer is fine.


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