Indices, Laws to Indices, Math Assignment Help

mathematics - Indices, Laws to Indices, Math


If a be any real number and n is the natural number, then

an = a × a × a x ..... × a n factors and n is index of a and plural of index is indices.


Laws to Indices:

(i)      am × an = am+¸n ; a Î R+, m, n, Î N

(ii)     am ¸ an = am-n ,a Î R+, m, n, Î N

(iii)    (am)n = amn ; a Î R+, m, n. Î N

(iv)    (ab)n = anbn; ab Î R, n Î N

(v)     (a ¸ b)n = an + bn = bn  = an/bn; a, b Î R+, n Î N

(vi)    a0 = 1, Where a is non-zero real number

(vii)   a-n = 1/an; a Î R, n a non­-negative.

(viii)   If a and b are two positive real numbers and n a natural number, such that bn = a, then b = a1/n.

(ix)    If a is a positive real number and m and n are integers with n positive, then (1/an)m am/n

(x)     If a, b are positive real numbers and n a natural number, then

                   an/2 bn/2 =  (ab)n/2

          (xi)    If am = bm, then a = b

(xii)   If am = an, then m = n.


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