Worked Example 1
Simplify 3⁴ × 3³ ÷ 3⁵.
The bases are all the sameAll base 3, so the laws apply
Multiplying adds the indices3⁴ × 3³ = 3⁷
Dividing subtracts3⁷ ÷ 3⁵ = 3² = 9
Check the long way81 × 27 = 2187, and 2187 ÷ 243 = 9. Same answer, far less work.
Worked Example 2
Work out 2⁻³ and explain what the negative index does.
Follow the halving pattern8, 4, 2, 1, ½, ¼, ⅛
Read off the answer2⁻³ = 1/8
What the sign meansNot negative. The minus puts the base underneath: 1 over 2³.
A useful checkA negative index always gives an answer between 0 and 1 when the base is above 1.
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