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

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Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

11 Feb 2013, 08:50

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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)

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Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

11 Feb 2013, 08:54

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)

2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}.

Answer: A.
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Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

20 Feb 2013, 18:16

Bunuel wrote:

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)

2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}.

Answer: A.

I don't understand how you get 2*2^(K-1). I'm obviously missing something but can't figure it out. Can you please explain?

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Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

20 Feb 2013, 21:15

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mp2469 wrote:

Bunuel wrote:

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)

2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}.

Answer: A.

I don't understand how you get 2*2^(K-1). I'm obviously missing something but can't figure it out. Can you please explain?

2^3 = 2*2*2 = 2*2^2

Similarly, 2^{10} = 2*2^9 = 2^2*2^8 etc

Hence 2^k = 2*2^{k-1} = 2^2*2^{k-2} = 2^3*2^{k-3} etc

Another Approach: Number Plugging.

Put k = 1 in 2^k*5^{k-1}. You get 2^1*5^0 = 2

When you put k = 1 in the options, only option (A) gives you 2.
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Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink]

21 Feb 2013, 03:20

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mp2469 wrote:

Bunuel wrote:

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)

2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}.

Answer: A.

I don't understand how you get 2*2^(K-1). I'm obviously missing something but can't figure it out. Can you please explain?

Operations involving the same exponents:
Keep the exponent, multiply or divide the bases
a^n*b^n=(ab)^n

Thus, 2*2^{k-1}=2^{1+k-1}=2^k.

For more check here: math-number-theory-88376.html

Hope it helps.
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Re: Which of the following is equal to (2^k)(5^k − 1)? [#permalink] 21 Feb 2013, 03:20

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

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