[tex]( {11}^{2011} \times {4}^{1005} ) \div {[ { {(22}^{2} )}^{5} ]} ^{201} [/tex]
[tex] = [ {11}^{2011} \times { {(2}^{2}) }^{1005} ] \div {22}^{2 \times 5 \times 201} [/tex]
[tex] = ( {11}^{2011} \times {2}^{2 \times 1005} ) \div ( {11 \times 2)}^{2010} [/tex]
[tex] = ( {11}^{2011} \times {2}^{2010} ) \div ( {11}^{2010} \times {2}^{2010} )[/tex]
[tex] = ( {11}^{2011} \div {11}^{2010} ) \times ( {2}^{2010} \div {2}^{2010} )[/tex]
[tex] = {11}^{2011 - 2010} \times {2}^{2010 - 2010} [/tex]
[tex] = {11}^{1} \times {2}^{0} [/tex]
[tex] = 11 \times 1[/tex]
[tex] = 11[/tex]
