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10^k + 5^k =

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Math Expert
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10^k + 5^k =  [#permalink]

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New post 22 Mar 2018, 22:46
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (00:29) correct 24% (00:30) wrong based on 61 sessions

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Re: 10^k + 5^k =  [#permalink]

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New post 22 Mar 2018, 23:00
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)



Formula used: \((a*b)^m = a^m * b^m\)

\(10^k + 5^k = (5*2)^k + 5^k = 5^k*2^k + 5^k = 5^k(2^k + 1)\) (Option B)
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Re: 10^k + 5^k =  [#permalink]

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New post 22 Mar 2018, 23:04
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


We'll show two approaches to solution:

The first relies on simplification and is a Precise approach.
Since 10^k = (5*2)^k = (5^k)(2^k) then we can extract a common factor of 5^k
from the original equation to get (5^k)(2^k+1).

If we don't feel too confident with the algebraic manipulations, we can instead just pick easy numbers.
This is an Alternative approach.

Say k = 2 then 10^k + 5^k = 100 + 25 = 125.
A. 5(4 + 1) = 25 NO
B. 25(4 + 1) = 125 Maybe, let's check the others.
C. 25*9 = 225 NO
D. 15^2 = 225 NO
E. 15^4 definitely not.

Either way, (B) is our answer.
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Re: 10^k + 5^k =  [#permalink]

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New post 23 Mar 2018, 04:39
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


=5^k(2^k+1)
Answer B
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10^k + 5^k =  [#permalink]

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New post 23 Mar 2018, 08:54
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


Key formula to use: \((a*b)^{m} = a^{m} * b^{m}\)

\(10^{k} + 5^{k} = 2^{k}*5^{k} + 5^{k} = 5^{k}*(2^{k} + 1) (B)\)
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Re: 10^k + 5^k =  [#permalink]

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New post 26 Mar 2018, 16:35
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


10^k + 5^k = 2^k * 5^k + 5^k = 5^k(2^k + 1)

Answer: B
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Re: 10^k + 5^k = &nbs [#permalink] 26 Mar 2018, 16:35
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