Quick Notes

Quick Notes

Mathematics Chapter 1: Indices
1.1 Index Notation
 
1.1  Index Notation
 
  • Index notation is written as \(a^n\), which \(a\) is the base and \(n\) is the index or exponent.
 
  Example  
     
 

\(2^3 = 2 \times 2 \times 2 \)

  • \(2^3\) (\(2\) to the power of \(3\)) is written in index notation which is the base is \(2\) and \(3\) is the index or exponent.

  
 
Repeated multiplication method:
 

\(2^3 = 2 \times 2 \times 2\)

  • The value of index is \(3\).

  • The value of index is the same as the number of times \(2\) is multiplied repeatedly.
 
  Example  
     
  (i)   \(5^4 = 5 \times5 \times 5\times 5\)  
         
  (ii)   \(0.3^3 = 0.3 \times 0.3 \times 0.3\)  
 
Repeated division method:
 
  • A number can be written in index form if a suitable base is used.
 
  Example  
     
 

Write \(32\) in index form using base of \(2\).

  
     
 

The base is \(2\)\(​​\).

So, \(32\) is divided repeatedly by \(2\).

The division is continued until \(1\) is obtained.

\(\begin{aligned}32 \div2&= 16 \\16 \div 2 &=8 \\8 \div 2&= 4 \\4 \div 2 &=2 \\ 2\div 2&=1.\\\\\end{aligned}\)

Thus, \(32=2^5\).