The powers of $$3$$

Algebra Level 1

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

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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