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.
Indices, Laws of Indices, Math Homework Help
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