Q1. Evaluate: 23
(a) 2
(b) 4
(c) 8
(d) 6
Ans: (c)
Sol: 23
= 2 × 2 × 2
= 8.
Q2. Simplify: 52 × 53
(a) 10
(b) 25
(c) 125
(d) 625
Ans: (c)
Sol: 52 × 53
= 25 × 125
= 125.
Q3. Evaluate: 40
(a) 0
(b) 1
(c) 4
(d) 2
Ans: (b)
Sol: Any non-zero number raised to the power of 0 is 1. So, 40 = 1.
Q4. Simplify: (22)3
(a) 6
(b) 8
(c) 64
(d) 16
Ans: (c)
Sol: (22)3
= 43
= 4 × 4 × 4
= 64.
Q5. Evaluate: 10(-2)
(a) 100
(b) 0.01
(c) 0.1
(d) 0.001
Ans: (b)
Sol: 10(-2)
= 1 / 102 = 1 / 100
= 0.01.
Q6. Simplify: (32) × (34)
(a) 9
(b) 81
(c) 243
(d) 729
Ans: (c)
Sol: (32) × (34)
= 9 × 81
= 243.
Q7. Evaluate: 15
(a) 5
(b) 1
(c) 0
(d) 6
Ans: (b)
Sol: Any non-zero number raised to the power of 0 is 1. So, 15 = 1.
Q8. Simplify: 61 × 62
(a) 12
(b) 18
(c) 36
(d) 72
Ans: (c)
Sol: 61 × 62
= 6 × 36
= 36.
Q9. Evaluate: 03
(a) 0
(b) 1
(c) 3
(d) 27
Ans: (a)
Sol: Any number (except 0) raised to the power of 0 is 1. However, 0^0 is undefined. So, 03 = 0.
Q10. Simplify: (23) ÷ (22)
(a) 1/2
(b) 2
(c) 4
(d) 8
Ans: (b)
Sol: (23) ÷ (22)
= 8 ÷ 4
= 2.
Q11. Evaluate: 5(-3)
(a) -125
(b) 125
(c) -25
(d) 1/125
Ans: (d)
Sol: 5(-3)
= 1 / 53
= 1 / 125.
Q12. Simplify: (72) × (7(-1))
(a) 1/49
(b) 7
(c) 49
(d) 1/7
Ans: (d)
Sol: (72) × (7(-1))
= 49 × 1/7
= 1.
Q13. Evaluate: (-3)4
(a) -81
(b) 81
(c) -27
(d) 27
Ans: (b)
Sol: (-3)4
= (-3) × (-3) × (-3) × (-3)
= 81.
Q14. Simplify: (2(-3)) × (2(-2))
(a) 1/4
(b) 1/8
(c) 1/16
(d) 1/64
Ans: (c)
Sol: (2(-3)) × (2(-2))
= 1/8 × 1/4
= 1/32.
Q15. Evaluate: (-2)3
(a) -8
(b) -2
(c) 8
(d) 2
Ans: (a)
Sol: (-2)3
= (-2) × (-2) × (-2)
= -8.
Q16. Simplify: (3(-2)) ÷ (3(-3))
(a) 1/9
(b) 1/6
(c) 1/27
(d) 1/81
Ans: (d)
Sol: (3(-2)) ÷ (3(-3))
= 1/9 ÷ 1/27
= 1/9 × 27/1
= 27/9
= 1/81.
Q17. Evaluate: (-1)0
(a) 0
(b) -1
(c) 1
(d) -2
Ans: (c)
Sol: Any non-zero number raised to the power of 0 is 1. So, (-1)0 = 1.
Q18. Simplify: (4(-1)) × (4(-2))
(a) 1/2
(b) 1/16
(c) 1/8
(d) 1/64
Ans: (b)
Sol: (4(-1)) × (4(-2))
= 1/4 × 1/16
= 1/64.
Q19. Evaluate: (-5)2
(a) -25
(b) 25
(c) -10
(d) 10
Ans: (b)
Sol: (-5)2
= (-5) × (-5)
= 25.
Q20. Simplify: (2(-2)) ÷ (2(-3))
(a) 1/2
(b) 2
(c) 1/4
(d) 8
Ans: (d)
Sol: (2(-2)) ÷ (2(-3))
= 1/4 ÷ 1/8 = 1/4 × 8
= 2.
Q21. Evaluate: (-3)2
(a) -9
(b) 9
(c) -6
(d) 6
Ans: (b)
Sol: (-3)2
= (-3) × (-3)
= 9.
Q22. Simplify: (3(-3)) × (3(-2))
(a) 1/9
(b) 1/6
(c) 1/18
(d) 1/54
Ans: (d)
Sol: (3(-3)) × (3(-2))
= 1/27 × 1/9
= 1/243.
Q23. Evaluate: (-4)3
(a) -12
(b) -64
(c) 64
(d) -8
Ans: (b)
Sol: (-4)3
= (-4) × (-4) × (-4)
= -64.
Q24. Simplify: (5(-2)) ÷ (5(-3))
(a) 1/5
(b) 1/25
(c) 1/125
(d) 5
Ans: (d)
Sol: (5(-2)) ÷ (5(-3))
= 1/25 ÷ 1/125
= 1/25 × 125/1
= 5.
Q25. Evaluate: (-2)4
(a) 8
(b) -8
(c) 16
(d) -16
Ans: (c)
Sol: (-2)4
= (-2) × (-2) × (-2) × (-2)
= 16.
Q26. Simplify: (3(-4)) × (3(-2))
(a) 1/6
(b) 1/18
(c) 1/81
(d) 1/324
Ans: (d)
Sol: (3(-4)) × (3(-2))
= 1/81 × 1/9
= 1/729.
Q27. Evaluate: (-1)10
(a) 0
(b) -1
(c) 1
(d) 10
Ans: (c)
Sol: Any non-zero number raised to the power of 0 is 1. So, (-1)10 = 1.
Q28. Simplify: (2(-4)) ÷ (2(-3))
(a) 1/2
(b) 1/8
(c) 1/16
(d) 1/32
Ans: (c)
Sol: (2(-4)) ÷ (2(-3))
= 1/16 ÷ 1/8
= 1/16 × 8/1
= 1/2.
Q29. Evaluate: (-5)3
(a) -125
(b) 125
(c) -25
(d) 25
Ans: (a)
Sol: (-5)3
= (-5) × (-5) × (-5)
= -125.
Q30. Simplify: (3(-2)) ÷ (3(-3))
(a) 1/3
(b) 3
(c) 1/9
(d) 9
Ans: (d)
Sol: (3(-2)) ÷ (3(-3))
= 1/9 ÷ 1/27
= 1/9 × 27/1
= 3.
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