mathematics - Indices, Laws to Indices, Math

INDICES

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)      a^m × aⁿ = a^m+¸n ; a Î R⁺, m, n, Î N

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

(iii)    (a^m)ⁿ = a^mn ; 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 = a^1/n.

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

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

                   a^n/2 b^n/2 =  (ab)^n/2

          (xi)    If a^m = b^m, then a = b

(xii)   If a^m = aⁿ, then m = n.

 

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