Each of the following equations has at least one solution EXCEPT

[B BTGmoderatorDC]

Each of the following equations has at least one solution EXCEPT

A. –2^n = (–2)^-n
B. 2^-n = (–2)^n
C. 2^n = (–2)^-n
D. (–2)^n = –2^n
E. (–2)^-n = –2^-n


OA A

Source: Manhattan Prep

[S swerve]

Each of the following equations has at least one solution EXCEPT

A. –2^n = (–2)^-n
B. 2^-n = (–2)^n
C. 2^n = (–2)^-n
D. (–2)^n = –2^n
E. (–2)^-n = –2^-n


OA A

Source: Manhattan Prep

Lets pick a value for \(n\).

\(n = 0\)

A. cannot be true as we get -1 on LHS and 1 on RHS ( as anything to the power of 0 is 1)
B. true (LHS = RHS = 1)
C. true (LHS = RHS = 1)
D. true (LHS = RHS = 1)
E. true (LHS = RHS = 1)

Hence, answer is A.