\[\large \left({\color{blue}3}^{23} - {\color{blue}3}^{22}\right)\left({\color{blue}3}^{24} - {\color{blue}3}^{23}\right) \left({\color{blue}3}^{25} - {\color{blue}3}^{24}\right)\]

This expression can be simplified as \({\color{red}2}^{\color{purple}m} \times {\color{blue}3}^{\color{teal}n}\).

What is \({\color{purple}m} + {\color{teal}n}?\)

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