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)^ma^m/n

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

a^n/2b^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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