Practice Maths

Problem Solving with Indices — Solutions

Click any answer to watch the solution video.

  1. Convert to scientific notation

  2. Convert from scientific notation to standard form

  3. Ascending order

  4. Calculate in scientific notation

    1. (3×104)×(2×103):
    2. (8×106)÷(4×102):
    3. (5×10−3)×(3×105):
    4. (9×108)÷(3×104):
    5. (4×103)2:
    6. (6×10−2)×(5×104):
    7. (2.4×105)÷(1.2×102):
    8. (7×104)×(3×10−6):

  5. Mixed index law problems

  6. Real-world problems

    1. 26 million:
    2. 1.496 × 108 km:
    3. 2 terabytes:
    4. Light in 60 s:
    5. Bank account:
    6. Atom masses:

  7. Valid scientific notation

    1. 3.5 × 104:
    2. 15 × 103:
    3. 0.7 × 106:
    4. 9.1 × 10−2:
    5. 10 × 105:
    6. 1.0 × 100:
    7. 6.28 × 10−7:
    8. 0.04 × 108:

  8. All index laws combined

    1. (32)4 × 32:
    2. 28 ÷ (23)2:
    3. (53)2 × 50 ÷ 54:
    4. [(42)3 × 41] ÷ 45:
    5. 37 × 3−3:
    6. 104 ÷ 107:

  9. Scientific notation with context

    1. Factory items in 30 days:
    2. File section size:
    3. Circumference of Earth:
    4. Molecules across 1 mm:

  10. Investigation: Powers and scale

    1. Hair vs DNA:
    2. Planet masses:
    3. (2.5×103)2:
    4. Research task: