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.

skauvzc 2022-09-23 Answered
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.
But in my situation, I'm not too sure how to tackle it.
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Answers (2)

Harold Beltran
Answered 2022-09-24 Author has 3 answers
2 n + 1 5 n 1 = 2 × 5 × 2 n 5 n = 10 × ( 2 5 ) n = 10 × 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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madeeha1d8
Answered 2022-09-25 Author has 1 answers
If the powers of the numerator and denominator matched, then you could combine them into a single fraction to that power.
a n b n = ( a b ) 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.
3 n 4 n 2 = 3 n 4 n 4 2 = 1 4 2 3 n 4 n = 4 2 1 3 n 4 n = 16 ( 3 4 ) n
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