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Which of the following is equal to (2^k)(5^k − 1)?
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11 Feb 2013, 07:50
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Which of the following is equal to 2^k*5^(k1)? A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1)
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Re: Which of the following is equal to (2^k)(5^k − 1)?
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11 Feb 2013, 07:54



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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20 Feb 2013, 17:16
Bunuel wrote: Which of the following is equal to 2^k*5^(k1)?
A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1)
\(2^k*5^{k1}=(2*2^{k1})*5^{k1}=2*10^{k1}\).
Answer: A. I don't understand how you get 2*2^(K1). I'm obviously missing something but can't figure it out. Can you please explain?



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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20 Feb 2013, 20:15
mp2469 wrote: Bunuel wrote: Which of the following is equal to 2^k*5^(k1)?
A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1)
\(2^k*5^{k1}=(2*2^{k1})*5^{k1}=2*10^{k1}\).
Answer: A. I don't understand how you get 2*2^(K1). I'm obviously missing something but can't figure it out. Can you please explain? \(2^3 = 2*2*2 = 2*2^2\) Similarly, \(2^{10} = 2*2^9 = 2^2*2^8\) etc Hence \(2^k = 2*2^{k1} = 2^2*2^{k2} = 2^3*2^{k3}\) etc Another Approach: Number Plugging. Put k = 1 in \(2^k*5^{k1}\). You get \(2^1*5^0 = 2\) When you put k = 1 in the options, only option (A) gives you 2.
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Re: Which of the following is equal to (2^k)(5^k − 1)?
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21 Feb 2013, 02:20



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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17 Jan 2014, 04:06
Bunuel wrote: Operations involving the same exponents:Keep the exponent, multiply or divide the bases \(a^n*b^n=(ab)^n\) Thus, \(2*2^{k1}=2^{1+k1}=2^k\). For more check here: mathnumbertheory88376.htmlHope it helps. Hey Karishma, Hey Bunuel, 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: \(2^k=2*2^{k1}\) I can simplify from k to k1. \(2^{k+1}=2*2^k\). 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 \(5^{k1}\) I have to see directly that I have to get all other exponents to k1?? I hope you get my question :D Thanks for your help Greetings!



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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20 Jan 2014, 01:48
unceldolan wrote: Bunuel wrote: Operations involving the same exponents:Keep the exponent, multiply or divide the bases \(a^n*b^n=(ab)^n\) Thus, \(2*2^{k1}=2^{1+k1}=2^k\). For more check here: mathnumbertheory88376.htmlHope it helps. Hey Karishma, Hey Bunuel, 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: \(2^k=2*2^{k1}\) I can simplify from k to k1. \(2^{k+1}=2*2^k\). 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 \(5^{k1}\) I have to see directly that I have to get all other exponents to k1?? 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 \(2^k=2*2^{k1}\) so you can easily get \(2^k\) down to \(2^{k1}\). Also, \(2^{k1} = 2^k/2\). So whether you bring the terms down to (k1) or (k) depends on the question. Here all options involve multiplication. Hence you will need to use \(2^k=2*2^{k1}\).
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Re: Which of the following is equal to (2^k)(5^k − 1)?
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20 Jan 2014, 02:24
unceldolan wrote: Bunuel wrote: Operations involving the same exponents:Keep the exponent, multiply or divide the bases \(a^n*b^n=(ab)^n\) Thus, \(2*2^{k1}=2^{1+k1}=2^k\). For more check here: mathnumbertheory88376.htmlHope it helps. Hey Karishma, Hey Bunuel, 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: \(2^k=2*2^{k1}\) I can simplify from k to k1. \(2^{k+1}=2*2^k\). 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 \(5^{k1}\) I have to see directly that I have to get all other exponents to k1?? I hope you get my question :D Thanks for your help Greetings! No, you could also change \(5^{k1}\) to \(\frac{5^{k}}{5}\) It is a bit more complicated but may help to understand. In this case, you would get \(2^{k}*5^{k1} = \frac{2^{k} * 5^{k}}{5} = \frac{10^{k}}{5} = \frac{10*10^{k1}}{5} = 2*10^{k1}\)
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Re: Which of the following is equal to (2^k)(5^k − 1)?
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12 Aug 2015, 23:36
4112019 wrote: Which of the following is equal to 2^k*5^(k1)?
A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1) 2^k*5^(k1)=10^k*5^1 option (A) is correct 2*10^(k1) = 10^k*5^1



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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15 Aug 2015, 07:43
Bunuel wrote: Which of the following is equal to 2^k*5^(k1)?
A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1)
\(2^k*5^{k1}=(2*2^{k1})*5^{k1}=2*10^{k1}\).
Answer: A. Is the following also correct ? 2^k x 5^(k1) = 2^(k) x 5^(k) x 5^(1) = 10^(k)/5 ?



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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17 Aug 2015, 23:53
mike34170 wrote: Bunuel wrote: Which of the following is equal to 2^k*5^(k1)?
A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1)
\(2^k*5^{k1}=(2*2^{k1})*5^{k1}=2*10^{k1}\).
Answer: A. Is the following also correct ? 2^k x 5^(k1) = 2^(k) x 5^(k) x 5^(1) = 10^(k)/5 ? Yes it is but it doesn't match any of the given options. So you need to split the numerator as \(10*10^{k  1}/5 = 2*10^{k  1}\)
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Re: Which of the following is equal to (2^k)(5^k − 1)?
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08 Mar 2016, 06:21



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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11 Sep 2017, 07:43
4112019 wrote: Which of the following is equal to 2^k*5^(k1)?
A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1) \(2^k*5^{(k1)}\) Simplifying the expression we get; \(2^k*\frac{5^k}{5}\) \(\frac{2^k*5^k}{5}\) \(\frac{(2*5)^k}{5} = \frac{10^k}{5}\) Check the options; (A) \(2*10^{(k1)} = 2*\frac{10^k}{10} = \frac{10^k}{5}\) Answer (A)...



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Re: Which of the following is equal to (2^k)(5^k − 1)?
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10 Feb 2019, 09:38
4112019 wrote: Which of the following is equal to 2^k*5^(k1)?
A. 2*10^(k1) B. 5*10^(k1) C. 10^k D. 2*10^k ) E. 10^(2k1) Question is \(2^k\) \(5^{k1}\) [\(2^k\) \(5^k\)] / 5 A) 2 * 10^k * 1/10 [\(2^k\) \(5^k\)] / 5
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Re: Which of the following is equal to (2^k)(5^k − 1)?
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