Rules Of Indices

Introduction
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Four important rules of indices are:

  • Rule of Multiplication
  • Rule of Division
  • Rule of Power of a Power
  • Rule of Powers of Brackets





Four important rules of indices are listed in table 1. Rules of multiplication and division are applied for indices containing identical base.

No.        Rules of indices Examples
1 Rule of Multiplication
am×an=am+n
23×24=23+4=27
2 Rule of Division
am÷an=amn
34÷32=342=32
3 Rule for power of a power
(am)n=am×n
(42)3=42×3=46
4 Rule of Powers of Brackets
(ambncp)r=am×rbn×rcp×r
(3ab2c2)2=32a2b222c2×2=9a2b24c4

Other important rules - applied for indices containing different base.
No.        Rules of indices Examples
1 Different base but similar power
am×bm=(a×b)mcn÷dn=(cd)n
e3×f3=(e×f)3=(ef)3
2 Zero Power
a0=1
60=1
3 Negative Power
1am=am
142=42
4 Rule of Root
man=anm
3a2=a23

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