On $EXP^{EXP}$?

  1. Does $ EXP^{EXP}=EXP$ ?

  2. Does $ EXP^{NP}\subseteq EXP^{EXP}$ ?

Note both $ 1.$ and $ 2.$ is not known to be same simultaneously or else we have $ EXP^{NP}\subseteq EXP^{EXP}=EXP\subseteq EXP^{NP}$ . This gives $ EXP^{NP}=EXP$ which is not known.