Exponentiation mistake

Algebra Level 3

Murray doesn't really understand how to exponentiate negative numbers. He thinks that negative numbers are aliens from another planet that he can't be bothered with, so he writes

\[ (-a)^b = a^b. \]

How many of the \( 10 \times 10 \) ordered pairs of integers \( (a, b) \), each of which are between 1 and 10 inclusive, satisfy

\[ (-a)^b = a^b ? \]

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