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A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?

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A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?  [#permalink]

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New post 21 Jan 2019, 23:32
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[Math Revolution GMAT math practice question]

\(A = (2-3+4)^{11}\), and \(B = (-2+3-4)^{11}.\) What is the value of \(2^{A+B}\)?

\(A. \frac{1}{2048}\)
\(B. \frac{1}{1024}\)
\(C. 1\)
\(D. 1024\)
\(E. 2048\)

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Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?  [#permalink]

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New post 22 Jan 2019, 08:40
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(A = (2-3+4)^{11}\), and \(B = (-2+3-4)^{11}.\) What is the value of \(2^{A+B}\)?

\(A. \frac{1}{2048}\)
\(B. \frac{1}{1024}\)
\(C. 1\)
\(D. 1024\)
\(E. 2048\)



\(A = (2-3+4)^{11}\) = \(A = (3)^{11}\) = X ( say)
Hence , \(B = (-2+3-4)^{11}.\)= \(B = (-3)^{11}.\) = -X
now \(A+B= X+(-X)= 0\)
\(2^{A+B}\) = \(2^{0}\) = \(1\) ...... Answer C
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Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?  [#permalink]

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New post 22 Jan 2019, 09:25
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(A = (2-3+4)^{11}\), and \(B = (-2+3-4)^{11}.\) What is the value of \(2^{A+B}\)?

\(A. \frac{1}{2048}\)
\(B. \frac{1}{1024}\)
\(C. 1\)
\(D. 1024\)
\(E. 2048\)


\(A = (2-3+4)^{11}\), and \(B = (-2+3-4)^{11}\)

\(A = (3)^{11}\), and \(B = (-3)^{11}\)

\(2^{A+B}\) = [m]A = 2^{3^11- 3^11}

2^0

Answer C
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Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?  [#permalink]

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New post 22 Jan 2019, 09:44
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(A = (2-3+4)^{11}\), and \(B = (-2+3-4)^{11}.\) What is the value of \(2^{A+B}\)?

\(A. \frac{1}{2048}\)
\(B. \frac{1}{1024}\)
\(C. 1\)
\(D. 1024\)
\(E. 2048\)



A= 3^11 and B= -3^11


2^A+B
=> 2^ ( 3-3)^11
=>2^0
=>1
IMO C
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Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?  [#permalink]

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New post 22 Jan 2019, 09:56
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(A = (2-3+4)^{11}\), and \(B = (-2+3-4)^{11}.\) What is the value of \(2^{A+B}\)?

\(A. \frac{1}{2048}\)
\(B. \frac{1}{1024}\)
\(C. 1\)
\(D. 1024\)
\(E. 2048\)


Note, (-2+3-4) =-1*(2-3+4) Therefore 2^A+B = 2^((2-3+4)^11-1^11(2-3+4)11) = 2^*((2-3+4)^11-(2-3+4)^11) = 2^0 =1 Answer is C
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Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?  [#permalink]

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New post 24 Jan 2019, 05:28
=>

\(A + B\)
\(= (2-3+4)^{11}+ (-2+3-4)^{11}\)
\(= 3^{11}+ (-3)^{11}\)
\(= 3^{11}- 3^{11}\)
\(= 0.\)
Therefore,
\(2^{A+B} = 2^0 = 1.\)

Therefore, the answer is C.
Answer: C
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Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?   [#permalink] 24 Jan 2019, 05:28
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