Index Notation — Solutions

1. Write in Index Notation

   1. 4 × 4 × 4: 4³ ▶ View Solution
   2. 7 × 7: 7² ▶ View Solution
   3. 2 × 2 × 2 × 2 × 2 × 2: 2⁶ ▶ View Solution
   4. 10 × 10 × 10: 10³ ▶ View Solution
   5. 5 × 5 × 5 × 5: 5⁴ ▶ View Solution
   6. 6 × 6: 6² ▶ View Solution
   7. 3 × 3 × 3 × 3: 3⁴ ▶ View Solution
   8. 9 × 9 × 9: 9³ ▶ View Solution

2. Evaluate Powers

   1. 2³: 8 ▶ View Solution
   2. 3²: 9 ▶ View Solution
   3. 4³: 64 ▶ View Solution
   4. 5²: 25 ▶ View Solution
   5. 10³: 1 000 ▶ View Solution
   6. 2⁵: 32 ▶ View Solution
   7. 6²: 36 ▶ View Solution
   8. 3³: 27 ▶ View Solution
   9. 7²: 49 ▶ View Solution
   10. 2⁶: 64 ▶ View Solution
   11. 4²: 16 ▶ View Solution
   12. 10⁵: 100 000 ▶ View Solution

3. Write as Repeated Multiplication

   1. 5⁴: 5 × 5 × 5 × 5 ▶ View Solution
   2. 3⁵: 3 × 3 × 3 × 3 × 3 ▶ View Solution
   3. 2⁷: 2 × 2 × 2 × 2 × 2 × 2 × 2 ▶ View Solution
   4. 6³: 6 × 6 × 6 ▶ View Solution
   5. 10⁴: 10 × 10 × 10 × 10 ▶ View Solution
   6. 4⁵: 4 × 4 × 4 × 4 × 4 ▶ View Solution
   7. 8²: 8 × 8 ▶ View Solution
   8. 9³: 9 × 9 × 9 ▶ View Solution

4. Compare and Order Powers

   1. 2³ vs 3²: 3² is larger ▶ View Solution
   2. 2⁵ vs 5²: 2⁵ is larger ▶ View Solution
   3. 2⁴ = 4²?: True — both equal 16 ▶ View Solution
   4. 3⁴ = 4³?: False — 3⁴ = 81, 4³ = 64 ▶ View Solution
   5. Order 2⁴, 4², 3³, 2⁵: 2⁴ = 4² < 3³ < 2⁵ ▶ View Solution

5. Patterns with Powers

   1. 2⁴, 2⁵, 2⁶ and pattern: 16, 32, 64 — each term doubles ▶ View Solution
   2. 2¹⁰: 1 024 ▶ View Solution
   3. 10³, 10⁴, 10⁵: 1 000; 10 000; 100 000 ▶ View Solution
   4. Pattern in 10ⁿ: n zeros after the 1 ▶ View Solution

6. Problem Solving with Powers

   1. Bacteria doubling 6 times (2⁶): 64 bacteria ▶ View Solution
   2. 2¹⁰ kilobytes: 1 024 kilobytes ▶ View Solution
   3. Area of 7 cm square: 49 cm² ▶ View Solution
   4. Volume of 4 cm cube: 64 cm³ ▶ View Solution
   5. 2⁸ vs 8²: 2⁸ is greater by 192 ▶ View Solution

7. Zero and One as Exponents

   1. 6⁰: 1 ▶ View Solution
   2. 10⁰: 1 ▶ View Solution
   3. 99⁰: 1 ▶ View Solution
   4. 5¹: 5 ▶ View Solution
   5. 13¹: 13 ▶ View Solution
   6. 4⁰ + 3¹: 4 ▶ View Solution
   7. 7¹ × 2⁰: 7 ▶ View Solution
   8. 5⁰ + 5¹ + 5²: 31 ▶ View Solution

8. Mixed Index Expressions

   1. 2³ + 3²: 17 ▶ View Solution
   2. 4² − 2³: 8 ▶ View Solution
   3. 2⁴ × 3: 48 ▶ View Solution
   4. 5² + 4²: 41 ▶ View Solution
   5. 3³ − 4²: 11 ▶ View Solution
   6. 2 × 3³: 54 ▶ View Solution
   7. (2 + 3)²: 25 ▶ View Solution
   8. 2² + 2³ + 2⁴: 28 ▶ View Solution

9. Index Notation — Composite Expressions

   1. Area of 9 cm square: 81 cm² ▶ View Solution
   2. Volume of 5 cm cube: 125 cm³ ▶ View Solution
   3. 3⁴ rows in display: 81 rows ▶ View Solution
   4. 1 000 000 as a power of 10: 10⁶ ▶ View Solution
   5. Smallest n where 2ⁿ > 100: n = 7 ▶ View Solution

10. Index Notation in Science and Technology

    1. 2⁸ files: 256 files ▶ View Solution
    2. Phone tree round 4 (3⁴): 81 people ▶ View Solution
    3. 5 × 3⁴ bacteria: 405 bacteria ▶ View Solution
    4. 1.5 × 10⁸ km in standard form: 150 000 000 km ▶ View Solution