Question

Evaluate (-1) ×(-1) ×(-1) ×(-1)………..101 times

Answer 1

Answer:

-1 ^(101)

Answer is -1

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Answer 2

Therefore the value of (-1) × (-1) × (-1) × (-1)………..101 times is -1.

Given:

The number = (-1) ×(-1) ×(-1) ×(-1)………..101 times

To Find:

Evaluation of (-1) ×(-1) ×(-1) ×(-1)………..101 times

Solution:

The given question can be answered very easily as shown below.

Given number = (-1) ×(-1) ×(-1) ×(-1)………..101 times

⇒ (-1) × (-1) = (-1)² = 1

⇒ (-1) × (-1) × (-1) = (-1)³ = -1

Hence we can conclude that,

⇒ (-1)ⁿ = 1 if n is even

⇒ (-1)ⁿ = -1 if n is odd

Now in the given question,

⇒ (-1) × (-1) × (-1) × (-1)………..101 times = (-1)¹⁰¹ = -1 because n = 101 is odd.

Therefore the value of (-1) × (-1) × (-1) × (-1)………..101 times is -1.

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