SUBJECT:-

MATHEMATICS

13. INDICES13. INDICES13. INDICES13. INDICES

Index13.1 Integeral indices.13.2 Fractional indices.13.3 Rules of indices.13.4 Examples.

Revision Revision Formula Formula--

1. 1. a×a×a×a×a×aa×a×a×a×a×a=a⁶=a⁶

2. 2. a �×aa �×ann =(a)=(a)m+n m+n

3.(a × b)ᵐ =aᵐ×aᵐ

4.(am)n=(a)mán

5.am aⁿ=aᵐ⁻ⁿ (if m>n)

6.a⁰=17.a⁻m=1/aᵐ

There are two ways to write the square root of a number :By using the symbol ‘√ ’ and by writing ½ as the index of the number. For example ,

The square root of 49 ‘ can be written as,√49 or 49½ .

There are two ways to write the square root of a number :By using the symbol ‘√ ’ and by writing ½ as the index of the number. For example ,

The square root of 49 ‘ can be written as,√49 or 49½ .

The index ½ represents the square root of a number & the index 1/3 represents the cube root of the number.

For example,1. 81/2 =The square root of 8= √8.

2. 125⅓= The cube root of 125= 3√125.

B) Rules of indices

The rules that apply to number with natural number indices also apply to numbers with fractional indices. You will understand this from the following solved examples.

Creation