Investigating Exponents For positive integers m and n, we
Chapter 0, Problem P.1.75(choose chapter or problem)
Investigating Exponents For positive integers m and n, we can use the definition to show that \(a^m a^n = a^{m+n}\).
(a) Examine the equation \(a^m a^n = a^{m+n}\) for n = 0 and explain why it is reasonable to define \(a^0 = 1\) for \(a\ \neq\ 0\).
(b) Examine the equation \(a^m a^m = a^{m+n}\) for n = -m and explain why it is reasonable to define \(a^{-m} = 1/a^m\) for \(a\ \neq\ 0\).
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