Salut!
Exercițiul 1:
a)
[tex]( \dfrac{21}{10} + {\dfrac{1}{2} }^{(5} ) \div \dfrac{13}{4} - \dfrac{6}{5} + 0.4 = \\ \\ \\ ( \dfrac{21}{10} + \dfrac{5}{10} ) \div \dfrac{13}{4} - \dfrac{6}{5} + {\dfrac{4}{10}}^{(2} = \\ \\ \\ { \dfrac{26}{10} }^{(2} \times \dfrac{4}{13} - \dfrac{6}{5} + \dfrac{2}{5} = \\ \\ \\ \dfrac{13}{5} \times \dfrac{4}{13} - \dfrac{6}{5} + \dfrac{2}{5} = \\ \\ \\ \dfrac{4}{5} - \dfrac{6}{5} + \dfrac{2}{5} = \\ \\ \\ - \dfrac{2}{5} + \dfrac{2}{5} = 0[/tex]
b)
[tex]{ ( \dfrac{5}{3} )}^{5} \times {( \dfrac{5}{3} } ) ^{2} )^{7} \div {( \dfrac{5}{3}) }^{16} = \\ \\ \\ {( \dfrac{5}{3} )}^{5} \times {( \dfrac{5}{3}) }^{2 \times 7} \div {( \dfrac{5}{3}) }^{16} = \\ \\ \\ {( \dfrac{5}{3} )}^{5} \times {( \dfrac{5}{3}) }^{14} \div {( \dfrac{5}{3}) }^{16} = \\ \\ \\ {( \dfrac{5}{3} )}^{5 + 14} \div {( \dfrac{5}{3} )}^{16} = \\ \\ \\ {( \dfrac{5}{3} )}^{19} \div {( \dfrac{5}{3}) }^{16} = \\ \\ \\ {( \dfrac{5}{3}) }^{19 - 16} = \\ \\ {( \dfrac{5}{3}) }^{3} = \dfrac{125}{27} [/tex]
Exercițiul 2:
[tex]a = ( \dfrac{3}{4} - ^{4)} 1) \times ( - 0.2) + \dfrac{3}{2} \\ \\ \\ a = ( \dfrac{3}{4} - \dfrac{4}{4} ) \times ( - \dfrac{2}{10} ) + \dfrac{3}{2} \\ \\ \\ a = ( - \dfrac{1}{4} ) \times ( - \dfrac{2}{10} ) + \dfrac{3}{2} \\ \\ \\ a = \dfrac{2}{40}^{(2} + \dfrac{3}{2} \\ \\ \\ a = \dfrac{1}{20} + \dfrac{3}{2}^{(10} \\ \\ \\ a = \dfrac{1}{20} + \dfrac{30}{20} = \dfrac{31}{20} [/tex]
[tex]b = \dfrac{15}{82} - \dfrac{15}{82} \times \dfrac{41}{3} \div \dfrac{5}{2} \\ \\ \\ b = \dfrac{15}{82} - ( -\dfrac{5}{2} ) \div \dfrac{5}{2} \\ \\ \\ b = \dfrac{15}{82}- (- \dfrac{5}{2}) \times \dfrac{2}{5} \\ \\ \\ b= \dfrac{15}{82}- ^{82)}1 \\ \\ \\ b= \dfrac{15}{82}- \dfrac{82}{82}= - \dfrac{67}{82} [/tex]
[tex]a=\dfrac{31}{20} , b=-\dfrac{67}{82} \\ \\ \\ a>b, a=pozitiv,b=negativ[/tex]
Exercițiul 3:
[tex]( - \dfrac{5}{4} )^{ - 2} \div ( - \dfrac{5}{4} ) ^{ - 6} \times (( - \dfrac{5}{4} )^{2})^{3} = \\ \\ \\ ( - \dfrac{5}{4} ) ^{ - 2 - ( - 6)} \times ( - \dfrac{5}{4} )^{2 \times 3} = \\ \\ \\ ( - \dfrac{5}{4} )^{ - 2 + 6} \times ( - \dfrac{5}{4} )^{6} = \\ \\ \\ ( - \dfrac{5}{4} )^{4} \times ( - \dfrac{5}{4} )^{6} = \\ \\ \\ ( - \dfrac{5}{4} ) ^{4 + 6} = ( - \dfrac{5}{4} )^{10} = \dfrac{5^{10} }{4 ^{10} } [/tex]
inversă:
[tex] \dfrac{4 ^{10} }{5 ^{10} } [/tex]
