PROF Math/Stat Concept

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The 8 laws of indices (also called laws of exponents or powers) are:

1. Product Law: a^m x a^n = a^m+n
Example: 3^2 x 3^4 = 3^(2+4) = 3^6 = 729

2. Quotient Law: a^m÷a^n = a^m-n
Example: 5^7 ÷ 5^4 = 5^(7-4) = 5^3 = 125

3. Power Law: (a^m)^n = a^mn
Example: (2^3)^4 = 2^(3x4) = 2^12 = 4,096

4. Negative Exponent Law: a^-n = 1 / a^n
Example: 2^-3 = 1 / 2^3 = 1/8

5. Zero Exponent Law: a^0 = 1
Example: 5^0 = 1

6. Product Power Law: (an)^m= a^m×n^m
Example: (2×3)^2= 2^2×3^2.

7. Root Power Law : a^1/n= (n✓a)
Example:a^1/2 =(✓a)

8. Fractional Exponent Law: a^(m/n) = n√(a^m)
Example: 64^(2/3) = 3√(64^2) = 16

These laws apply to any positive real numbers (a, m, n), unless otherwise stated.