Indices I
O Level and IGCSE Mathematics Quiz: Indices I
Non-Calculator Section
1. What is the value of 2⁰?
A. 0
B. 1
C. 2
D. Undefined
2. Evaluate: 7⁻²
A. 49
B. 1⁄49
C. –49
D. 1⁄7
3. What is the value of 8¹⁄³?
A. 2
B. 4
C. 8
D. 3
4. Simplify: 2⁻³ × 2⁴
A. 2
B. 1
C. 8
D. 16
5. Simplify: (3²)³
A. 9
B. 27
C. 81
D. 729
6. What is 5⁻¹ × 5³?
A. 1
B. 5
C. 25
D. 125
7. Simplify: 10² ÷ 10⁵
A. 10⁷
B. 10³
C. 10⁻³
D. 10⁻⁷
8. Evaluate: (2³)²
A. 64
B. 32
C. 16
D. 8
9. Simplify: 6³ × 6⁻¹
A. 6
B. 36
C. 216
D. 6²
10. What is the value of 9¹⁄²?
A. 3
B. 4.5
C. 81
D. 1.5
11. Simplify: a⁶ ÷ a²
A. a²
B. a⁴
C. a³
D. a⁸
12. What is the value of (4⁻¹)⁻²?
A. ¹⁄₁₆
B. ¹⁄₄
C. 16
D. 4
13. Simplify: x⁰ + y⁰
A. x + y
B. 0
C. 2
D. 1
14. Evaluate: (5⁻²) × (5³)
A. 5
B. ¹⁄₂₅
C. 25
D. 5⁵
15. Simplify: (2a³b²)²
A. 4a⁶b⁴
B. 4a⁵b⁴
C. 4a³b²
D. 2a⁶b²
Calculator-Allowed Section
16. Evaluate: 27¹⁄³ × 9¹⁄²
A. 6
B. 9
C. 3
D. 81
17. Simplify: (8⁻²) × (8⁵)
A. 8³
B. 8⁷
C. 8⁻³
D. 8⁻¹⁰
18. What is the value of 16⁻¹⁄²?
A. 4
B. –4
C. 1⁄4
D. 1⁄2
19. Evaluate: (3²)⁻³
A. 1⁄729
B. 1⁄81
C. 9
D. 729
20. Simplify: a⁻³b² ÷ a⁻¹b⁻²
A. a⁻²b⁴
B. a⁻⁴b⁴
C. a⁻²b⁻⁴
D. a²b⁴
21. What is the value of 64⁰.⁵ × 2⁻³?
A. 1
B. 0.5
C. 2
D. 4
22. Simplify: (x²y)⁻³
A. x⁶y³
B. x⁻⁶y⁻³
C. x⁻⁶y³
D. x⁶y⁻³
23. Evaluate: 100⁰ × 10³
A. 0
B. 1000
C. 1
D. 100
24. Simplify: (5a²)⁻²
A. 1⁄25a⁴
B. 1⁄25a⁻⁴
C. 1⁄(25a⁴)
D. 25⁄a⁴
25. What is the value of 81⁻³⁄⁴?
A. 1⁄27
B. 1⁄9
C. 1⁄3
D. 1⁄√3
26. Evaluate: 4⁻³ × 2⁴
A. 1⁄4
B. 1
C. 1⁄2
D. 2
27. Simplify: (x³ ÷ x⁵) × x²
A. x⁴
B. x²
C. x⁰
D. x
28. What is the value of 32⁰.²?
A. 1
B. 4
C. 2
D. 5
29. Simplify: (2⁵ × 2⁻⁷) ÷ 2⁻³
A. 2
B. 2¹
C. 2²
D. 2³
30. Evaluate: (1⁄4)⁻²
A. 1⁄8
B. 1⁄2
C. 16
D. 8
Answer key and explanations
O Level and IGCSE Mathematics Quiz: Indices I
1. Correct Answer: B
Explanation:
2⁰ = 1 because any non-zero number raised to the power 0 is 1.
2. Correct Answer: B
Explanation:
7⁻² = 1 ÷ 7² = 1⁄49.
3. Correct Answer: A
Explanation:
8¹⁄³ = ∛8 = 2.
4. Correct Answer: A
Explanation:
2⁻³ × 2⁴ = 2^(–3 + 4) = 2¹ = 2.
5. Correct Answer: D
Explanation:
(3²)³ = 9³ = 729.
6. Correct Answer: C
Explanation:
5⁻¹ × 5³ = 5^(–1 + 3) = 5² = 25.
7. Correct Answer: C
Explanation:
10² ÷ 10⁵ = 10^(2 – 5) = 10⁻³.
8. Correct Answer: A
Explanation:
(2³)² = 2^(3×2) = 2⁶ = 64.
9. Correct Answer: D
Explanation:
6³ × 6⁻¹ = 6^(3 – 1) = 6².
10. Correct Answer: A
Explanation:
9¹⁄² = √9 = 3.
11. Correct Answer: B
Explanation:
a⁶ ÷ a² = a^(6 – 2) = a⁴.
12. Correct Answer: C
Explanation:
(4⁻¹)⁻² = 4^(–1 × –2) = 4² = 16.
13. Correct Answer: C
Explanation:
x⁰ = 1 and y⁰ = 1 → x⁰ + y⁰ = 1 + 1 = 2.
14. Correct Answer: A
Explanation:
5⁻² × 5³ = 5^(–2 + 3) = 5¹ = 5.
15. Correct Answer: A
Explanation:
(2a³b²)² = 2² × a⁶ × b⁴ = 4a⁶b⁴.
16. Correct Answer: A
Explanation:
27¹⁄³ = 3 and 9¹⁄² = 3 → 3 × 3 = 9.
17. Correct Answer: A
Explanation:
8⁻² × 8⁵ = 8^(–2 + 5) = 8³.
18. Correct Answer: C
Explanation:
16⁻¹⁄² = 1 ÷ √16 = 1 ÷ 4 = 1⁄4.
19. Correct Answer: A
Explanation:
(3²)⁻³ = 9⁻³ = 1 ÷ 729 = 1⁄729.
20. Correct Answer: A
Explanation:
a⁻³b² ÷ a⁻¹b⁻² = a^(–3 – (–1)) × b^(2 – (–2)) = a⁻²b⁴.
21. Correct Answer: A
Explanation:
64⁰.⁵ = √64 = 8; 2⁻³ = 1⁄8 → 8 × 1⁄8 = 1.
22. Correct Answer: B
Explanation:
(x²y)⁻³ = x⁻⁶y⁻³.
23. Correct Answer: B
Explanation:
100⁰ = 1 and 10³ = 1000 → 1 × 1000 = 1000.
24. Correct Answer: C
Explanation:
(5a²)⁻² = 1 ÷ (25a⁴) = 1⁄(25a⁴).
25. Correct Answer: A
Explanation:
81⁻³⁄⁴ = 1 ÷ (⁴√81)³ = 1 ÷ 3³ = 1⁄27.
26. Correct Answer: A
Explanation:
4⁻³ = 1⁄64, 2⁴ = 16 → 16 ÷ 64 = 1⁄4.
27. Correct Answer: C
Explanation:
x³ ÷ x⁵ = x⁻² → x⁻² × x² = x⁰ = 1.
28. Correct Answer: C
Explanation:
32⁰.² = ⁵√32 = 2.
29. Correct Answer: B
Explanation:
(2⁵ × 2⁻⁷) ÷ 2⁻³ = 2^(5 – 7 + 3) = 2¹ = 2.
30. Correct Answer: C
Explanation:
(1⁄4)⁻² = 4² = 16.