# Thread: Which of the following is equal to (2^k)(5^(k-1))?

1. Good post? |

## Which of the following is equal to (2^k)(5^(k-1))?

A. 2(10^(k-1))
B. 5(10^(k-1))
C. 10^k
D. 2(10^k)
E. 10^(2k-1)

OA in a few...

2. Good post? |
(2^k)(5^(k-1) = 2*{2^(k-1)}*{5^(k-1)}
= 2*{(2*5)^(k-1)}
= 2*{10^(k-1)}
Hence A.

3. Good post? |
Originally Posted by linfongyu
A. 2(10^(k-1))
B. 5(10^(k-1))
C. 10^k
D. 2(10^k)
E. 10^(2k-1)

OA in a few...
Hi Im a new user for this community. If there is something wrong please feel free to correct it.

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.

4. Good post? |
2 * 2^(k-1) * 5(k-1)
= 2 * (2*5)^(k-1)
=2 * (10)^(k-1)