Topic Review — Index Notation — Solutions

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1. Index notation fluency

   1. 8⁵
   2. 128
   3. 10 000
   4. 6 × 6 × 6
   5. 4
   6. 32

2. Multiplication and division index laws

   1. 3⁹
   2. 7⁶
   3. 5¹²
   4. 2⁴
   5. 4⁸
   6. 6

3. Negative indices and mixed index laws

   1. 19
   2. 132
   3. □ = 5
   4. □ = 5
   5. Yes — both sides equal 216
   6. 2

4. Scientific notation

   1. 4.75 × 10⁶
   2. 6.2 × 10⁻⁵
   3. 5 300 000
   4. 0.00021
   5. 9.1×10⁴, 3.8×10⁵, 4.2×10⁵
   6. 2 × 10⁸

5. Problem solving

   1. 280 times wider
   2. 1
   3. 64 cm = 0.64 m
   4. $40 000 per person