A)
[tex]1 + {3}^{2} - 4 = 1 + 9 - 4 = 10 - 4 = 6[/tex]
[tex]5 \times {2}^{3} + 1 = 5 \times 8 + 1 = 40 + 1 = 41[/tex]
B)
[tex]2 + {(5 + {2}^{2}) }^{3} \div 9 = 2 + {(5 + 4)}^{3} \div 9 = 2 + {9}^{3} \div 9 = 2 + {9}^{3 - 1} = 2 + {9}^{2} = 2 + 81 = 83[/tex]
[tex]12 \div ( {2}^{3} - 2) + 1 = 12 \div (8 - 2) + 1 = 12 \div 6 + 1 = 2 + 1 = 3[/tex]
C)
[tex] {3}^{2} - ( {3}^{2} - ( {3}^{2} - (1 + 2 \times 3))) = 9 - (9 - (9 - (1 + 6))) = 9 - (9 - (9 - 7)) = 9 - (9 - 2) = 9 - 7 = 2[/tex]
[tex] {5}^{2} + {4}^{2} - {( {3}^{2} - {2}^{3} )}^{20} = 25 + 16 - {(9 - 8)}^{20} = 41 - {1}^{20} = 41 - 1 = 40[/tex]
