[tex]a) \\
2^8 \cdot 4^{12} \cdot 8^{32} : 16^{32} = \\
=2^8 \cdot (2^2)^{12} \cdot (2^3)^{32} : (2^4)^{32} = \\
=2^8 \cdot 2^{2 \times 12} \cdot 2^{3 \times 32} : 2^{4 \times 32} = \\
=2^8 \cdot 2^{24} \cdot 2^{96} : 2^{128} = 2^{8+24+96-128} =2^{128-128} = \boxed{2^0} =\boxed{1} [/tex]
[tex]b) \\
5^8 \cdot 9^3 \cdot 25^2 : 5^{10} : 3^6 = \\
=5^8 \cdot 25^2 : 5^{10} \cdot 9^3 : 3^6 = \\
=5^8 \cdot (5^2)^2 : 5^{10} \cdot (3^2)^3 : 3^6 = \\
=5^8 \cdot 5^{2 \times 2} : 5^{10} \cdot 3^{2 \times 3} : 3^6 = \\
=5^8 \cdot 5^4 : 5^{10} \cdot 3^6 : 3^6 = \\
=5^{8+4-10} \times 3^{6-6} = 5^{2} \times 3^{0} = 5^{2} \times 1 = \boxed{5^{2}}
\\ \\ \\ \\ ngn[/tex]
