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

[linfongyu]

A. 2(10^(k-1))

B. 5(10^(k-1))

C. 10^k

D. 2(10^k)

E. 10^(2k-1)

 

Please show your steps.

 

OA in a few...

[12rk34]

(2^k)(5^(k-1) = 2*{2^(k-1)}*{5^(k-1)}

= 2*{(2*5)^(k-1)}

= 2*{10^(k-1)}

Hence A.

:)

[vipakorn]

A. 2(10^(k-1))

B. 5(10^(k-1))

C. 10^k

D. 2(10^k)

E. 10^(2k-1)

 

Please show your steps.

 

OA in a few...

 

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

[MBAchase]

answer is A

2 * 2^(k-1) * 5(k-1)

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

=2 * (10)^(k-1)