Asking about a union of languages and how they interact

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if we take a language, $L= \{b^{2n}a^n \mid n \gt 0\} \cup \{b^{3n}a^n \mid n \gt 0\}$

would this be the same as $L=\{b^{2n}a^n b^{3n} a^n \mid n \gt 0\}$ ?

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Hint. Does the word $b^2ab^3a$ belongs to your language?