How can I show that the language is regular using the closure properties?

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How can I show that the language $L=\{ w \in \{a,b\}^*: \text{ the word w contains an even number of a and an odd number of b} \}$ is regular using the closure properties?

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Suppose $A$ is the set of words that have an even number of as, and $B$ is the set of words that have an odd number of bs. Then $L = A\cap B$. Do you know anything about regular languages and intersections?