How attacking this question?
Show that if $A$ and $B$ are sets such that $A$ is infinite, $|A|+|A|=|A|$, and $|B|\geq 2$, then $|B^A|+|B^A|=|B^A|$
How attacking this question?
Show that if $A$ and $B$ are sets such that $A$ is infinite, $|A|+|A|=|A|$, and $|B|\geq 2$, then $|B^A|+|B^A|=|B^A|$
The $\geq$ part is obvious; and to show $\leq$ simply show that the following holds: $|B^A|+|B^A|\leq|B^A|\times|B^A|=|B^{A+A}|=|B^A|$
Now use Cantor-Bernstein to finish the job.