a
(a) \({a^x}.{a^y}.{a^z} = {(x + y + z)^{y + z + x}}\)

\( \Rightarrow \,\,{a^{x + y + z}} = {(x + y + z)^{x + y + z}}\)\( \Rightarrow \) \(x + y + z = a\)

Now, \({a^x} = {(x + y + z)^y} = {a^y}\)\( \Rightarrow \) \(x = y\), similarly \(y = z\)

\(\therefore x = y = z = {a \over 3}\).