# Simplifying exponential fraction I have this exponential fraction (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 (2^(n+1))/(2^(n+1)), you would just subtract the exponent.

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.
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Harold Beltran
$\frac{{2}^{n+1}}{{5}^{n-1}}=2×5×\frac{{2}^{n}}{{5}^{n}}=10×{\left(\frac{2}{5}\right)}^{n}=10×{0.4}^{n}$ if you wish. But if you are dealing with simplifying fractions, I do think your answer is fine.
###### Did you like this example?
If the powers of the numerator and denominator matched, then you could combine them into a single fraction to that power.
$\frac{{a}^{n}}{{b}^{n}}={\left(\frac{a}{b}\right)}^{n}$
In your case we need to manipulate the fraction a bit first since the powers don't match.
I will show you how to do this with a similar example. You can then try it on your own problem.
$\frac{{3}^{n}}{{4}^{n-2}}=\frac{{3}^{n}}{{4}^{n}{4}^{-2}}=\frac{1}{{4}^{-2}}\frac{{3}^{n}}{{4}^{n}}=\frac{{4}^{2}}{1}\frac{{3}^{n}}{{4}^{n}}=16{\left(\frac{3}{4}\right)}^{n}$