Which of the following is equal to

[linfongyu]

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)

Please show your steps.

OA in a few...

[gmat740]

Very Simple solution:

(2^k)(5^(k-1))
This can be written as

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

As we can always write: M^a+b = (^a).(^b)
where (.) represents Multiplication
So (2^k)(5^k)/5
10^k/5
Now multiply numerator and dinominator both by 2
2[10^k/10]

2[10^k-1]

Answer A

[linfongyu]

Thanks for the solve. I got to as far as here, then I was stuck: 10^k/5

I'm not very good at manipulating algebraic/exponential expressions... I need to work on this.

[Stuart@KaplanGMAT]

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)

Please show your steps.

OA in a few...

Slightly different approach:

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

so:

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

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

and since x^a * y^a = (x*y)^a,

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

= 2 * 10^(k-1)

[gmat740]

Glad to help you
I think by practice you can improve your skills.