Evaluate: (1)4, (1)5, (1)7, (- 1)2, (- 1)3, (- 1)4, (- 1)5

1.	Evaluate: (1)4, (1)5, (1)7, (- 1)2, (- 1)3, (- 1)4, (- 1)5
Answer» (1)⁴= 1 × 1 × 1 × 1 = 1 (1)⁵= 1 × 1 × 1 × 1 × 1 = 1 (1)⁷= 1 × 1 × 1 × 1 × 1 × 1 × 1 = 1 (- 1)²= (-1) × (-1) = 1 (- 1)³= (-1) × (1) × (-1) = – 1 (- 1)⁴=(-1) × (-1) × (-1) × (-1) = 1 (- 1)⁵= (-1) × (-1) × (-1) × (-1) × (- 1) = – 1 From the above illustrations, (i) It raised. to any power is 1. (ii) (-1) raised to even power is (- 1) and (-1) raised to an odd power is (-1). Thus (- 1)^m = 1 if ’m’ is even (- 1)^m 1 if ‘m’ is odd

Answer»

(1)⁴= 1 × 1 × 1 × 1 = 1

(1)⁵= 1 × 1 × 1 × 1 × 1 = 1

(1)⁷= 1 × 1 × 1 × 1 × 1 × 1 × 1 = 1

(- 1)²= (-1) × (-1) = 1

(- 1)³= (-1) × (1) × (-1) = – 1

(- 1)⁴=(-1) × (-1) × (-1) × (-1) = 1

(- 1)⁵= (-1) × (-1) × (-1) × (-1) × (- 1) = – 1

From the above illustrations,

(i) It raised. to any power is 1.

(ii) (-1) raised to even power is (- 1) and (-1) raised to an odd power is (-1).

Thus (- 1)^m = 1 if ’m’ is even (- 1)^m 1 if ‘m’ is odd

Discussion