Exponent ( Indices )

 An index or power is a mathematical representation that indicates the number of times that a number is multiplied by itself.

If a number is multiplied by itself m times, then it can be written as: a x a x a x a x a…m times = am. Here, a is called the base, and m is called the exponent or power or index.

Indices are a useful way of more simply expressing large numbers. They also present us with many useful properties for manipulating them using what are called the Law of Indices. Let us look at these laws in this topic.

Definitions

The index of a number is the number which shows how many times that number has occurred in the term as a repeated factor

an implies that the number a is multiplied by itself n number of times, where n is a positive integer

a is called the base and n is called the index or exponent or power.

Law Of Indices ( exponent)

• am×an=am+n 
  • 23×24=23+4= 27
    

• (a×b)m=am×bm
  
  • (2×5)3=23×53

• am÷an=am−n 
  • 24÷23=24−3 = 21
    

• (ab)m=ambm
  
  • (25)3=2353
    

• (a m)n=amn
  • (22)3= 22×3=26
    

• a−n=1an
  
  • 2−3=123

• a1n=a−−√n
  
  • 213=2–√3

  amn=(a−−√n)m

  • 223=(2–√3)2
    

• a0=1
  
  • 20=1 An

• a1=a
  
  • 21=2