> Does \$$(X \rightarrow Y) \times B = X \times B \rightarrow Y \times B \$$?

Not in general, no. Not even for any Cartesian Closed Domain.

> Does \$$(X \rightarrow Y)^B = X^B \rightarrow Y^B \$$?

Not in general, no. Not even for any Cartesian Closed Domain.

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However, in a Cartesian Closed Domain we **do** have:

\$(X \to Y)^B \cong X \to (Y^B) \$