Explicație pas cu pas:
[tex]a) \: ({2}^{3} \times {3}^{2} - {6}^{2} ) \div {2}^{2} + 2 \\ \\ (8 \times 9 - 36) \div 4 + 2 \\ \\ (72 - 36) \div 4 + 2 \\ \\ 36 \div 4 + 2 \\ \\ 9 + 2 \\ \\ \boxed{11}[/tex]
[tex] (({15}^{2} \div 5 - {3}^{2} ) + 12) \div 6 \\ \\( (225 \div 5 - 9) + 12) \div 6 \\ \\ ((45 - 9) + 12) \div 6 \\ \\ (36 + 12) \div 6 \\ \\ 48 \div 6 \\ \\ \boxed{8}[/tex]
[tex]c) \: (( {2}^{3})^{4} \div ({2}^{5})^{2} + ({5}^{3})^{7} \div ({5}^{4})^{5}) \div 3 - 3 \\ \\ ( {2}^{3 \times 4} \div {2}^{5 \times 2} + {5}^{3 \times 7} \div {5}^{4 \times 5}) \div 3 - 3 \\ \\ ({2}^{12} \div {2}^{10} + {5}^{21} \div {5}^{20} ) \div 3 - 3 \\ \\ ( {2}^{12 - 10} + {5}^{21 - 20} ) \div 3 - 3 \\ \\ ( {2}^{2} + {5}^{1} ) \div 3 - 3 \\ \\ (4 + 5) \div 3 - 3 \\ \\ 9 \div 3 - 3 \\ \\ 3 - 3 = \boxed{0}[/tex]
[tex]d) \: {3}^{2} \times 5 - {2}^{4}\div 2 \\ \\ 9 \times 5 - {2}^{4 - 1} \\ \\ 45 - {2}^{3} \\ \\ 45 - 8 = \boxed{ 37}[/tex]
[tex]e) \: 3 \times ( {5}^{2} - {4}^{2}) - 6 \\ \\ 3 \times (25 - 16) - 6 \\ \\ 3 \times 9 - 6 \\ \\ 27 - 6 = \boxed{21}[/tex]
