Exponent

Exponent

Points to be Remember:-

1.   If a rational number then a x a x a x ….. x a (n times) = aⁿ. Here

     is the base and n is the exponent.        

2.   We can write the exponent of a rational number as the 

     exponents of numerator and denominator separately. For  

     example ( p )ⁿ = pⁿ

                    q        qⁿ

Points to be Remember:-

1.   If a rational number then

a^m x aⁿ  =  (a x a x …. M times)  x  (a x a x …. N times)

                =  (a x a x a …… m + n times) = a^{m + n}

Or     a^m x aⁿ  = a^{m + n}

2.   If a ( ≠ 0 ) is a rational number, and m and n are two positive integers such that:

 (i) m > n then a^m ¸ aⁿ = a^{m – n}

 (ii) m < n then a^m ¸ aⁿ =   1          

                                     a^{n – m}

    3.  (a^m)ⁿ = a^{m x n} = a^mn

Points to be Remember:-

1. a^-m  = ( 1 )^m

                a        or

     ( a ) ^–m  =  ( b )^m 

       b              a

2.  x⁰ = 1

3. If a and b are any two integers or rational numbers ( ≠ 0 ) and m is 

    an integer, then (a x b)^m = a^m x b^m and

   (a x b)^-m = a^-m x b^-m

Points to be Remember:-

Large and small numbers can be expressed in the form of k x 10n, where k is a terminating decimal number and n is an integer (positive for large number and negative for small number). In general we choose k in such a way that 1£ k < 10.