Quantity B is always 1

Quantity A
2n + 1 is an odd number. So -1^(2n + 1) is negative

If n is negative whole expression is positive else negative

A is either equal to B or lesser than B. Cannot be Determined

Option D

OE


Note that −1 and 1, when raised to an integer power, have very limited possibilities. Negative 1 raised to an even power is 1, and −1 raised to an odd power is −1, whereas 1 raised to a power is always 1. Therefore, this is really a problem about odds and evens. So plug in a small even number and a small odd number and try to prove (D). If n = 2, Quantity A is equal to (−1)^5 × (−1)^2, which is −1, and Quantity B is equal to 1. If n = 3, Quantity A is equal to (−1)^7 × (−1)^3, which is 1, and Quantity B is equal to 1. Stop here—the answer is (D).
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Hey,

Is -1^n and (-1)^ n equal? If n = 2, then -1^2 = -1 and (-1)^2 = 1.