Question

calculati (dau coroană)​

Answer 1

Răspuns:

${10}^{60} \div (2 \times 5) ^{58} = {10}^{60} \div {10}^{58} = {10}^{2} = 100 \\ ( { {7}^{14} \times 5) }^{2} \div {7}^{26} = \\ = { {(7 }^{14} })^{2} \times {5}^{2} \div {7}^{26} = {7}^{28} \times {5}^{2} \div {7}^{26} = {7}^{2} \times {5}^{2} = (7 \times 5 )^{2} = {35}^{2} = 1225$

$( {7}^{6} ) ^{8} \div {49}^{24} = {7}^{48} \div {(7}^{2} ) ^{24} = {7}^{48} \div {7}^{48} = 1 \\ {( {3}^{4} })^{9} \div ({9}^{6} ) ^{3} = {3}^{36} \div {9}^{18} = {3}^{36} \div ( {3}^{2} ) ^{18} = {3}^{36} \div {3}^{36} = 1$

$( {11}^{2011} \times {4}^{1005} ) \div {(((22)}^{2} ){5}^{201} ) = \\ = ( {11}^{2011} \times ({2}^{2} )1005) \div ({22}^{2 \times 5 \times 201} ) = \\ = ( {11}^{2011} \times {2}^{2010} ) \div {22}^{2010} = \\ = ( {11}^{2011} \times {2}^{2011 - 1} ) \div {22}^{2010} = \\ = ( {11}^{2011} \times {2}^{2011} \div {2}^{1} ) \div {22}^{2010} \\ = (( {11 \times 2})^{2011 } \div 2) \div {22}^{2010} \\ = ( {22}^{2011} \div 2) \div {22}^{2010} = \\ = \frac{ {22}^{2011} \div 2 }{ {22}^{2010} } = {22}^{1} \div 2 = 22 \div 2 = 11$