Question

(11la puterea2011 •4 la puterea 1005):[(22la puterea2) la puterea 5]la puterea 201

Answer 1

$( {11}^{2011} \times {4}^{1005} ) \div {[ { {(22}^{2} )}^{5} ]} ^{201}$

$= [ {11}^{2011} \times { {(2}^{2}) }^{1005} ] \div {22}^{2 \times 5 \times 201}$

$= ( {11}^{2011} \times {2}^{2 \times 1005} ) \div ( {11 \times 2)}^{2010}$

$= ( {11}^{2011} \times {2}^{2010} ) \div ( {11}^{2010} \times {2}^{2010} )$

$= ( {11}^{2011} \div {11}^{2010} ) \times ( {2}^{2010} \div {2}^{2010} )$

$= {11}^{2011 - 2010} \times {2}^{2010 - 2010}$

$= {11}^{1} \times {2}^{0}$

$= 11 \times 1$

$= 11$