\[\boxed{\text{547\ (547).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ 4^{5} \cdot 2^{21} = \left( 2^{2} \right)^{5} \cdot 2^{21} =\]
\[= 2^{10} \cdot 2^{21} = 2^{10 + 21} = 2^{31}\]
\[\textbf{б)}\ 25^{13}\ :5^{11} = \left( 5^{2} \right)^{13}\ :5^{11} =\]
\[= 5^{26}\ :5^{11} = 5^{26 - 11} = 5^{15}\]
\[\textbf{в)}\ 8^{5} \cdot 16^{13} = \left( 2^{3} \right)^{5} \cdot \left( 2^{4} \right)^{13} =\]
\[= 2^{15} \cdot 2^{52} = 2^{15 + 52} = 2^{67}\]
\[\textbf{г)}\ 27^{10}\ :9^{15} = \left( 3^{3} \right)^{10}\ :\left( 3^{2} \right)^{15} =\]
\[= 3^{30}\ :3^{30} = 3^{30 - 30} = 3^{0}\]