Index Notation

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, \(32=2^5\).