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Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions:
\(2^k=2*2^{k-1}\) I can simplify from k to k-1. \(2^{k+1}=2*2^k\). I can simplify from k+1 to k
BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like \(5^{k-1}\) I have to see directly that I have to get all other exponents to k-1??
I hope you get my question :D Thanks for your help
Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions:
\(2^k=2*2^{k-1}\) I can simplify from k to k-1. \(2^{k+1}=2*2^k\). I can simplify from k+1 to k
BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like \(5^{k-1}\) I have to see directly that I have to get all other exponents to k-1??
I hope you get my question :D Thanks for your help
Greetings!
What you need to do in any question depends on that particular question.
You know that \(2^k=2*2^{k-1}\) so you can easily get \(2^k\) down to \(2^{k-1}\). Also, \(2^{k-1} = 2^k/2\). So whether you bring the terms down to (k-1) or (k) depends on the question. Here all options involve multiplication. Hence you will need to use \(2^k=2*2^{k-1}\).
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Karishma Veritas Prep GMAT Instructor
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Till now, I have encountered this kind of problem several times. Am I right to assume that these are the rules for simplifiying expontents like those in the questions:
\(2^k=2*2^{k-1}\) I can simplify from k to k-1. \(2^{k+1}=2*2^k\). I can simplify from k+1 to k
BUT I CAN'T simplify the first equation "backwards" meaning that if I see a exponent like \(5^{k-1}\) I have to see directly that I have to get all other exponents to k-1??
I hope you get my question :D Thanks for your help
Greetings!
No, you could also change \(5^{k-1}\) to \(\frac{5^{k}}{5}\) It is a bit more complicated but may help to understand.
In this case, you would get \(2^{k}*5^{k-1} = \frac{2^{k} * 5^{k}}{5} = \frac{10^{k}}{5} = \frac{10*10^{k-1}}{5} = 2*10^{k-1}\)
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71% (01:32) correct 
