1971 AHSME Problems/Problem 7

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Problem

$2^{-(2k+1)}-2^{-(2k-1)}+2^{-2k}$ is equal to

$\textbf{(A) }2^{-2k}\qquad \textbf{(B) }2^{-(2k-1)}\qquad \textbf{(C) }-2^{-(2k+1)}\qquad \textbf{(D) }0\qquad  \textbf{(E) }2$

Solution

By using the properties of exponents, we can simplify the given expression as follows to obtain our answer: 2(2k+1)2(2k1)+22k=22k122k+1+22k=22k2222k+22k=22k(122+1)=22k(12)=22k2=22k1=(C) 2(2k+1).

See Also

1971 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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