Blog

Parin Sir > Quantitative Aptitude (Maths) > Surds & Indices > Surds & Indices

Surds & Indices

No Comments

Indices  :   we know that  2 \times 2  =  22,  2 \times 2 \times 2  =  23,  etc.

Generalising thus,  we have,

a \times a  =  a2,  a \times a \times a  =  a3,  a \times a \times a \times a  =  a4

a \times a \times a \times…15 times  =  a15

a \times a \times a \times…m  times  =  am

Hence,  we can say that by  am,  we mean   a \times a \times a … m times  i.e., the product of  m factors each equal to ‘a’ is represented by am.  ‘a’  is called the  base  and  m  is called the  index.

 

■ a^{m}\times a^{n}  =  a^{m+n}

e.g.  34 \times 35  =  34 + 5   =  39  =   19683

 

■  \frac{a^{m}}{a^{n}}  = a^{m-n}   ;  m > n,  a \ne 0.

e.g. \frac{5^{6}}{5^{4}}  = 5^{6-4} =  5^{2} =  25

 

■ \left (ab \right )^{m} =    a^{m}\times b^{m}

e.g.   \left (2\times 3 \right ) ^{5} =   2^{5} \times 3^{5}   =  7776

 

■ \left (\frac{a}{b} \right )^{m}= \frac{a^{m}}{b^{m}}  ;  b \ne0.

e.g. \left (\frac{3}{5} \right )^{5} =  \frac{3^{5}}{5^{5}}  = \frac{243}{3125}

 

■ \left (a^{m} \right )^{n} =  a^{mn} = \left (a^{n} \right )^{m}

e.g. \left (5^{2} \right )^{3}  =  56   =   15625

 

■ a0  =  1   :   a \ne 0.   (   \because 0^{0}   =  \infty   )

e.g.  80  = 1, \left (\frac{2}{5} \right )^{0} =  1;  (1.251)0 =  1

 

■  a^{-n}=   \frac{a}{a^{n}}   and   \frac{a}{a^{-n}}  =  a^{n}  :  a \ne 0   &   n  is  any  positive  integer.

e.g.    7^{-5}  = \frac{1}{7^{5}} ,  \frac{1}{5^{-3}}   = 5^{3}

 

Click here to see next topic

Share
educational formula maths sutra Examples mathematics sutr SUMS ganit Indices example concept math proof Parin theorem sir theorems bhai definition Mehta definitions maheta fundamental classes basic class base education sum online dakhla tutorial surds

Leave a Reply