IGCSE Indices Laws and Examples
Recap the basic laws of indices, raise terms to specific powers, solve equations using laws of indices, and test understanding with examples and exercises in this IGCSE indices lesson. Explore laws of indices forwards and backwards with practical explanations and visual aids provided by Dr. J. Frost.
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IGCSE Indices Dr J Frost (jfrost@tiffin.kingston.sch.uk) Objectives: Recap the basic laws of indices. Raise a term to a 3 2= 1 27 power. Use laws of indices backwards, e.g. solve ? Last modified: 16th August 2015
RECAP :: Basic Laws of Indices AQA Specimen 2 1 2 ? ?3 4 as a single power of ?. 3 2 Write ? ?2 ?12= ? 10 ? ?11 ?6 ? = ?9 ?10 Write ? in terms of ? and ?. Give your answer in its simplest form. ? =?9 ?10 ?11 ?6= ? 2 ?4 ?
RECAP :: Basic Laws of Indices 3 2= ? 3=? 3 2=? ? 4 8 1 ? ? ? ?? 4 5 ? 2= ? ? 3=? 27 2 1 ? 4 9 2=? ? ? 3 5= ? 2=? ? ? 32 25 1 2 3 27 8 =? ? ? ? ?
Law of Indices Backwards 3 4= 27 Solve ? The thinking backwards method The cancelling the power method. (DO THIS!) If I had some number to the power of 3 what would I do to it? 4, What power should I raise both sides of the equation to cancel the 3 4 power? Find the 4th root then cube it. ? ?= ?? ? ? ? ? ? ? ? So going backwards from 27: Cube root: 3 Raise to the power of 4: 81 ? ? ? = ?? ? = ??
Further Examples Solve ? 3= 33 Solve ? 2 3= 27 8 9 ?=?? ? ? ? ?=?? ? ? ? ? ? ? ? ?? ? ?? ??? ? ?? ? =? ? = = ? = ?
Test Your Understanding 2 3= 9 Solve ? ? ?= ?? ? ? = ? Solve ? 3 8 27 2= ? ? ? ?? =? ? ? = ?
RECAP :: Single terms to a power Simplify 3?2?3 2 9?4?6 ? 1 2 Simplify 9?4? 1 2 ? 3?2?
Exercises ? [June 2012 Paper 1] Simplify 2??4 3= ?????? [Set 1 Paper 2] You are given that ? = 5? and ? = 5?. (a) Write 5?+2 in terms of ?. ??? (b) Write 5? ? in terms of ? and ?. ? ? (c) Write 53? in terms of ?. ?? ?+? 2 in terms of ? and ?. ?? ?? ? ? 1 7 [Set 2 Paper 2] Write as single powers of ?: (a) ?12 ? 4= ??? 1 2 ? ? ? 2 ? ? 3 2= ?? (b) ? ? 1 ?6= ? ? (c) 3 2= 8 and ? 2=25 ?? ? = ? ? ? [June 2012 Paper 1] ? Work out the value of ? 4. ?= ?? 3 ? (d) Write 5 ? [June 2013 Paper 1] Simplify 3??5 4 4 ? = ??????? [Set 3 Paper 1] Simplify 20?9?6 4?3?2= ?? ??? 8 [June 2013 Paper 1] Solve ? 2 answer as a proper fraction. ?? ? 3= 71 ? 9 writing your 5 1 2= 6 and ? 3= 64 [Set 3 Paper 1] ? Work out the value of ? ? ? = ?? ? ??? 9 [June 2013 Paper 2] ? 2= ?6 ?4 Write ? in terms of ? and ?. Give your answer in its simplest form. ? = ?? ?? ? ? 6 ? ?= ??? ?= ? ? ? ? ?
