Laws of Positive Integral Indices 點解急急急急急急急急?

Laws of Positive Integral Indices (正整數指數定律)
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For any real nos. a, b and positive integers m, n :
1. (a^m)(a^n) = a^(m+n)
2. (a^m)/(a^n) = a^(m-n), for a≠0
3. (a^m)^n = a^(mn)
4. (ab)^n = (a^n)(b^n)
5. (a/b)^n = (a^n)/(b^n), for b≠0
6. a^0 = 1, for a≠0
7. a^(-n) = 1/(a^n), for a≠0

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egs. : -
Law 1:(a^m)(a^n) = a^(m+n)
eg. (7^3)(7^2) = 7^(3+2) = 7^5

Law 2: (a^m)/(a^n) = a^(m-n), for a≠0
eg. (7^5)/(7^3) = 7^(5-3) = 7^2

Law 3. (a^m)^n = a^(mn)
eg. (11^3)^2 = 11^(3×2) = 11^6

Law 4. (ab)^n = (a^n)(b^n)
eg. (3×7)^2 = (3^2)(7^2)

Law 5. (a/b)^n = (a^n)/(b^n), for b≠0
eg. (3/7)^2 = (3^2)/(7^2)

Law 6. a^0 = 1, for a≠0
eg. 2^0 = 1
eg. (1234)^0 = 1

Law 7. a^(-n) = 1/(a^n), for a≠0
eg. (7)^(-2) = 1/(7^2) = 1/49
eg. (2)^(-5) = 1/(2^5) = 1/32