Rewrite a number in index form and vice versa

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.

Repeated division method:

	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, \(32=2^5\).

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.

Repeated division method:

	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, \(32=2^5\).