[tex]a=1+7^{49}:(7\cdot 7^2 \cdot 7^{45})-(7^2+7\cdot 2):3^2=\\
=1+7^{49}:7^{1+2+45}-(49+14):9=\\
=1+7^{49}:7^{48}-63:9=1+7^{49-48}-63:9=1+7-7=1\\
\boxed{a=1}\\\\
b=12345-123\cdot 2^2 \cdot 5^2-2^3\cdot3^2\cdot5:8 =\\
=12345-123\cdot 4 \cdot 25-8\cdot9\cdot5:8 =\\
=12345-123\cdot 100-9\cdot5 =12345-12300-45 = 45-45=0\\
\boxed{b=0}\\\\
a^b = 1^0 = \boxed{1}\\
b^a = 0^1 = \boxed{0}[/tex]
