A5 $\operatorname{Expression}\left(\left(\left(a^{x+y}\right)^{x-y}\right)^{x^{2}+y^{2}}\right)^{x^{4}+y^{4}}$ can also be written in the form:
(A) $a^{x^{16}-y^{16}}$
(B) $a^{x^{6}-y^{6}}$
(C) $a$
(D) $x^{8}-y^{8}$
(E) $a^{x^{8}-y^{8}}$
A5. The expression $\left(\left(\left(a^{x+y}\right)^{x-y}\right)^{x^{2}+y^{2}}\right)^{x^{4}+y^{4}}$ is simplified. We start with the innermost parentheses, where we consider the product of the sum and difference $\left(\left(a^{x^{2}-y^{2}}\right)^{x^{2}+y^{2}}\right)^{x^{4}+y^{4}}$. We repeat the process, as in the next step we also use the product of the sum and difference $\left(a^{x^{4}-y^{4}}\right)^{x^{4}+y^{4}}$. In the final step, we also take into account the previous rule and obtain $a^{x^{8}-y^{8}}$.