[S2_20150513IXS] The Power of Repeated Chunks

Question

Introduction

     This is a question on indices (taught in secondary 2 or 3) that looks daunting.  There is a way to unravel it.  Look at the equation carefully.  Can you see anything that looks like it is repeated?  What about that small little “+1”?  How do you deal with it?

Reminders and Tips

    

Solution

Summary

     The key to solving this question is to apply the laws of indices and recognising repeated chunks.  This allows one to see the overall structure of the expression and this often leads to a simplification of the expression involved.  It is good to recognise the powers of small prime numbers.  Like atoms, prime numbers are the building blocks of all whole numbers.  Using prime bases allows us to compare indices more easily.

Heuristics Used

H04. Look for pattern(s)   e.g. repeated chunks

H09. Restate the problem in another way

H10. Simplify the problem

H11. Solve part of the problem

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* Lower Secondary Mathematics (usually Sec 2)

* “Elementary” Mathematics or “E Maths”

* Additional Mathematics (revision)

* other syllabuses that involve indices