Laws of Exponents are of following types
Multiplication of Same Base with Different Exponents (a^{m} X a^{n} = a^{m+n} )
Division of Same Base with Different Exponents (a^{m} a^{n} = a^{mn})
One Base with Exponent of Exponent[(a^{m} )^{n} = a^{m n} ]
Multiplication of different Bases with Same Exponent a^{m} X b^{m} = (ab)^{m}
Division of different Bases with Same Exponent a^{m} ÷ b^{m} = (a/b)^{m}
Base with Zero Exponent is always equal to 1 (a^{0} = 1)
Base with negative exponents i.e. a^{ m} = 1/m
All these Laws are explained with examples in the above respective links.

