Power of -1

Last updated at Dec. 16, 2024 by

Suppose we have

  (−1) 2 = −1 × −1

 = 1

 

  (−1) 3 = −1 × −1 × −1

 = 1 × −1

 = −1

 

  (−1) 4 = −1 × −1 × −1 × −1

 = 1 × 1

 = 1

 

  (−1) 5 = −1 × −1 × −1 × −1 × −1

 = 1 × 1 × −1

 = −1

 

  (−1) 6 = −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1

 = 1

 

  (−1) 7 = −1 × −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1 × −1

 = −1

 

  (−1) 8 = −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1

= 1 × 1 × 1 × 1

= 1

 

  (−1) 9 = −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1 × 1 × −1

 = −1

 

  (−1) 10 = −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1 × −1

 = 1 × 1 × 1 × 1 × 1 × 1

 = 1

 

So, we see that

  (−1) odd number = −1

  (−1) even number = 1

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo