(2^k)(5^(k-1) = 2*{2^(k-1)}*{5^(k-1)}
= 2*{(2*5)^(k-1)}
= 2*{10^(k-1)}
Hence A.
Hi Im a new user for this community. If there is something wrong please feel free to correct it.
The correct answer is A.
First: (2^k)(5^(k-1)) = (2^k)((5^k)/5^1)
Second: You can further simplify the exponential expression to:
((2^k)(5^k))/5
Third: ((2^k)(5^k)) can be simplified to ((2*5)^k) --> 10^k
Forth: So the most simplified expression is (10^k)/5
Fifth: Let's check at each choices and find out which one can be
simplified as same as (10^k)/5
Look at choice A: 2(10^(k-1))
This expression can be simplifed as follows:
2((10^k)/10^1)) --> 2(10^k))/10 --> (10^k)/5
That is exactly the same as what we could simplify from the questions.
So the answer is A
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