## 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, $$32=2^5$$.
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