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SFtraveler
- Junior | Next Rank: 30 Posts
- Posts: 21
- Joined: Mon Aug 30, 2010 11:51 am
5^k -5^(k-1) = 5^k(1 - 1*(-1/5)) = 6*5^k/5SFtraveler wrote:Please show each step in factoring: 5^k-5^(k-1)
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factoring exponents
Source: Beat The GMAT — Problem Solving |
Night reader wrote:5^k -5^(k-1) = 5^k(1 - 1*(-1/5)) = 6*5^k/5SFtraveler wrote:Please show each step in factoring: 5^k-5^(k-1)
Not sure how 5^k -5^(k-1) becomes 5^k(1 - 1*(-1/5))
It should be 5 ^k - 5^k/5 = 5^k(1-1/5) = 4/5 * 5^k or 4 * 5^k-1
I show the answer being (4/5) 5^k.
Everest, thank you for your answer. I messed up at 5^(k-1) = 5^k * 5^-1. I found the exponent rule (x^a)/(x^b) = x^(a-b) that covers doing that step.
Night reader, your answer is incorrect.
Everest, thank you for your answer. I messed up at 5^(k-1) = 5^k * 5^-1. I found the exponent rule (x^a)/(x^b) = x^(a-b) that covers doing that step.
Night reader, your answer is incorrect.
@SFTraveler I found this problem as well as the solution defined by you as correct one not confident...SFtraveler wrote:I show the answer being (4/5) 5^k.
Everest, thank you for your answer. I messed up at 5^(k-1) = 5^k * 5^-1. I found the exponent rule (x^a)/(x^b) = x^(a-b) that covers doing that step.
Night reader, your answer is incorrect.
-a^x is the same as (-a)^x, but not the same as -(a)^x
-5^(k-1) = -5^(k+ (-1)) = -5^k * -5^(-1) = -5^k * -1/5 = (5^k)/5
and 5^k -5^(k-1) = 6/5 *5^k
----------------------------
5^k -(5^(k-1)) = 4/5 *5^k
what's the source of this question?
check point
k=3
5^3 - 5^(3-1) = 125 -5^2 = 125+25= 150 <> 150= 6/5 * 5^3 OR 6*125/5 = 6*25 and not 4/5*5^3
5^3 -(5^(3-1))= 125 -(5^2) = 125-25 = 100 <> 4/5 * 5^3
check the statement in your book again, and tell us the source
Thank you, I am attaching the original slide from the BTG flashcards.SFtraveler wrote:Source is beatthegmat.com flashcards (factoring exponents example)
and I think we should ask Eric to have the above discussed statement corrected symbol-wise
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Thank you for pointing this out! I'll try to get this fixed shortly.
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