Indices (Copy)
Practice Questions — 1.7 Indices I
Question 1
Evaluate: 2³ × 2⁴
Question 2
Simplify: (3²)³
Question 3
Work out: 5⁷ ÷ 5³
Question 4
Evaluate: 7⁰
Question 5
Find the value of: 10⁻²
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Question 6
Simplify: (2⁵ × 2⁻³)
Question 7
Evaluate: (4³)²
Question 8
Simplify: (9⁴ ÷ 9²)
Question 9
Find the value of: (2⁻³) × (2⁴)
Question 10
Evaluate: 25¹/²
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Question 11
Evaluate: 8¹/³
Question 12
Simplify: (27¹/³)²
Question 13
Work out: 16³/⁴
Question 14
Simplify: (5²)⁻¹
Question 15
Evaluate: (2³ ÷ 2⁵)
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 16
Simplify fully: (a³ × a⁻⁵)
Question 17
Simplify: (x²)³ ÷ (x³)²
Question 18
Write as a single power of 2: 2⁴ × 2⁻⁷ ÷ 2⁻³
Question 19
If y = 81, evaluate y¹/² and y⁻¹/²
Question 20
Simplify: (p⁻² q³) × (p⁴ q⁻¹)
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 1.7 Indices I
1.
128
Explanation: 2³ × 2⁴ = 2⁷ = 128. (Same base, add powers.)
2.
729
Explanation: (3²)³ = 3⁶ = 729. (Power of a power, multiply powers.)
3.
625
Explanation: 5⁷ ÷ 5³ = 5⁴ = 625. (Same base, subtract powers when dividing.)
4.
1
Explanation: Any non-zero number to the power 0 equals 1: 7⁰ = 1.
5.
0.01 (or 1/100)
Explanation: 10⁻² = 1/(10²) = 1/100 = 0.01.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
4
Explanation: 2⁵ × 2⁻³ = 2² = 4.
7.
4096
Explanation: (4³)² = 4⁶. Since 4 = 2², 4⁶ = (2²)⁶ = 2¹² = 4096.
8.
81
Explanation: 9⁴ ÷ 9² = 9² = 81.
9.
2
Explanation: 2⁻³ × 2⁴ = 2¹ = 2.
10.
5
Explanation: 25¹/² means the square root of 25, which is 5.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
2
Explanation: 8¹/³ is the cube root of 8. Since 2³ = 8, 8¹/³ = 2.
12.
9
Explanation: (27¹/³)² = 27²/³. Cube root of 27 is 3, then 3² = 9.
13.
8
Explanation: 16³/⁴ = (⁴√16)³. ⁴√16 = 2, so 2³ = 8.
14.
1/25 (or 0.04)
Explanation: (5²)⁻¹ = 5⁻² = 1/(5²) = 1/25.
15.
1/4 (or 0.25)
Explanation: 2³ ÷ 2⁵ = 2⁻² = 1/2² = 1/4.
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16.
1/a²
Explanation: a³ × a⁻⁵ = a⁻² = 1/a² (for a ≠ 0).
17.
1
Explanation: (x²)³ ÷ (x³)² = x⁶ ÷ x⁶ = x⁰ = 1 (for x ≠ 0).
18.
1
Explanation: 2⁴ × 2⁻⁷ ÷ 2⁻³ = 2^(4−7+3) = 2⁰ = 1.
19.
y¹/² = 9, y⁻¹/² = 1/9
Explanation: If y = 81, then y¹/² = √81 = 9. So y⁻¹/² = 1/(y¹/²) = 1/9.
20.
p² q²
Explanation: (p⁻² q³)(p⁴ q⁻¹) = p^(−2+4) q^(3−1) = p² q².
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course