Scoretop 4 - No.18 - Factorization/Exponents

[akay]

I know this is easy for quite a few of you but I need some help with this...

Which of the following is equal to (2^k)(5^k-1)?
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5 to the power k - 1
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A. 2 (10^k-1) 10 to the power k - 1
B. 5 (10^k-1) 10 to the power k - 1
C. 10^k
D. 2(10^k)
E. 10^2k-1 10 to the power 2k - 1

[beny]

Realize that you can pull a 2 out of 2^k:
2^k = 2*2^(k-1)

Therefore,
2^k*5^(k-1) = 2*2^(k-1)*5(k-1)

(in bold above) Now realize that 2^(k-1)*5^(k-1) = 10^(k-1)

Therefore, the answer is A: 2*10^(k-1)

[akay]

tks for your time beny