Indices and Logarithms - I — O/L Mathematics

How do I practise Indices and Logarithms - I?

1 question with a worked solution

1. Simplify and find the value of: (27)^2/3 × (16)^1/2.
   1. A) 48
   2. B) 36
   3. C) 24
   4. D) 18
   Check my answer

   Correct answer: B) 36

   27^2/3 = (3³)^2/3 = 3² = 9. 16^1/2 = √16 = 4. Product = 9 × 4 = 36.

   Show worked solution

   Step 1: Express bases in prime power form: 27 = 3³ and 16 = 4² (or 2⁴). Step 2: Apply index law (a^m)ⁿ = a^mn: (3³)^2/3 = 3^{3 × 2/3} = 3² = 9. Step 3: (4²)^1/2 = 4^{2 × 1/2} = 4¹ = 4. Step 4: Multiply results: 9 × 4 = 36. Answer: 36.
   Modelled on: the O/L Mathematics examination pattern

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Where does Indices and Logarithms - I fit in the syllabus?

Grade 11 · Term 1