Practice Maths

Establishing Index Notation — Solutions

Click any answer to watch the solution video.

  1. Write in index notation

  2. Evaluate each expression

  3. Expanded form

    1. 54:
    2. 35:
    3. 73:
    4. 27:
    5. 104:
    6. 82:
    7. 43:
    8. 64:

  4. Zero and one powers

    1. 70:
    2. 151:
    3. 1000:
    4. (−3)0:
    5. 50 + 21:
    6. 41 × 30:
    7. 100 + 101 + 102:
    8. 60 × 61 × 62:

  5. Ascending order

    1. 25=32, 33=27, 52=25, 43=64:
    2. 102=100, 73=343, 210=1024, 54=625:
    3. 63=216, 92=81, 44=256, 28=256:
    4. 1100=1, 21=2, 30=1, 05=0:

  6. Real-world index notation

    1. Bacteria after 6 hours:
    2. Computer storage:
      1. 1 megabyte:
      2. Kilobytes in 1 gigabyte:
    3. Tile area:
      1. Area of one tile:
      2. Total area:
    4. Mia’s mistake:

  7. Base and index

    1. 75:
    2. 29:
    3. 106:
    4. 43:
    5. 81:
    6. 152:
    7. 67:
    8. 1000:

  8. Write and evaluate

    1. 8 × 8 × 8:
    2. 6 × 6:
    3. 1 × 1 × 1 × 1 × 1:
    4. 10 × 10 × 10 × 10:
    5. 5 × 5 × 5:
    6. 2 × 2 × 2 × 2 × 2 × 2 × 2:

  9. True or False

    1. 24 = 42:
    2. 32 > 23:
    3. 150 = 50:
    4. 50 = 0:
    5. 05 = 0:
    6. 25 < 52:
    7. 104 = 4 × 10:

  10. Patterns and powers

    1. Powers of 2:
      1. 21:
      2. 22:
      3. 23:
      4. 24:
      5. 25:
    2. Paper folds:
    3. 210 vs 102:
    4. Expressions equal to 64: