Topic 1: Indices

What is Indices?

Plural of index, written also as indexes.

Indices is a number when multiple by itself several times can be written in index notation.

Example of Indices:

Example 1:

2x2x2= 2³

2³ is called index notation.

2 is called the base and 3 is called power or index (indices) or the exponent.

2³ is read as ‘2 to the power of 3^’ or ‘the three power of 2’

Numbers in index notation with the same base such as 2², 2³,2⁴,2^23,2¹⁰⁰⁰, are referred to as powers of 5.

Example 2:  

[1]  2^-3 
     = ½³
     = 1/8

  

[2] (3/5)^-2 

    = (5/3)²
    = 5²/3²
    = 25/9

[3] Fraction index

           a^1/n 
    
       = ⁿ√a

          a^m/n 

       = ⁿ√a^m

Example 3: 

(ⁿ√a)^m

 25^1/2
= √25 
= 5

16 ^3/2

= (√16)³ 
= 4³

=64    

a^a/m   = m is power

         = n is root

[Roots always stay at the bottom]

                             Rules/Formula of Indices:                                

1) zero Index

         a⁰ = 1  

Examples: [1] 7⁰= 1

                   [2] (3/4)⁰=1

       2) Negative Index

            a^-m

           =1/a^m

          (a/b)^-m

          =(b/a)^m

SEE THIS VIDEO! (learn something from this video).....

SOLVE THIS QUESTIONS?

[Q1] a³ x a² =

[Q2] 2³ x 2⁴ =

[Q3] P³ x P^-4 =

[Q4] a⁴ ÷ a^1 =

[Q5] (a²)² =

[Q6]  (a²b⁴) =

[Q7] (a^ba x a^ba)^a =

[Q8] C² ÷ C⁴ =

[Q9] 3^x = 81

[Q10] 2^x =32