(-1)¹⁰⁰⁰ का मान है:

Question

(-1)¹⁰⁰⁰ का मान है:

1. A. -1
2. B. 1 (Correct answer)
3. C. 1000
4. D. -1000

Correct Answer

Option B — 1

Detailed Solution & Explanation

The correct answer is 1.

Key Points

• (−1) raised to an even power is +1; raised to an odd power it is −1.
• 1000 is even, so (−1)^1000 = 1.

Exam Tip

• Only the parity of the exponent matters, never its size. (−1)^999 = −1, (−1)^1000 = 1.

Additional Information

• The same parity rule governs signs generally: a product of an even number of negative factors is positive, an odd number negative.
• Related standard results: a⁰ = 1 (a ≠ 0), a⁻ⁿ = 1/aⁿ, and (−1)ⁿ + (−1)ⁿ⁺¹ = 0 for every integer n.