Do brackets make any difference?

Algebra Level 3

\[ \Large\left( \color{blue}{5}^{\color{green}{4}^{\color{purple}{3}}}\right)^{\color{magenta}{2}^{\color{orange}{1}}} \times \color{blue}{5}^{\left( \color{green}{4}^{\color{purple}{3}}\right)^{\color{magenta}{2}^{\color{orange}{1}}}} = \color{blue}{5}^{\color{red}{b}} \quad ; \quad \color{red}{b} = \ ?\]

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