a)
[tex] = ({3}^{2 \times 5} \div {3}^{7} - 1 - 9) \times 4 \div 34 + 4 = \\ = ({3}^{10 } \div {3}^{7} - 1 - 9) \times 4 \div 34 + 4 = \\ = ( {3}^{10 - 7} - 1 - 9) \times 4 \div 34 + 4 \\ = ( {3}^{3} - 1 - 9) \times 4 \div 34 + 4 = \\ = (27 - 1 - 9) \times 4 \div 34 + 4 = \\ = 17 \times 4 \div 34 + 4 = \\ = 68 \div 34 + 4 = \\ = 2 + 4 = \\ = 6[/tex]
b)
[tex](123 + {2}^{7 + 2} + {2}^{67 - 27}) \div (123 + {2}^{14 - 5} + {2}^{5 \times 8}) = \\ = (123 + {2}^{9} + {2}^{40} ) \div (123 + {2}^{9} + {2}^{40} ) = \\ = 1[/tex]
c)
[tex] = {25}^{4 \times 3} \div \: {(16 + 9)}^{11} - {(0 + 1 + 1)}^{2} = \\ = {25}^{12} \div {25}^{11} - {2}^{2} = \\ = {25}^{12 - 11} - 4 = \\ = 25 - 4 = \\ = 21[/tex]
d)
[tex] = (27 \times 3 + {2}^{45 - 42} + {3}^{5 \times 6} \div {3}^{29} + 1) \div 31 = \\ = (81 + {2}^{3} + {3}^{30} \div {3}^{29} + 1) \div 31 = \\ = (81 + 8 + {3}^{30 - 29} + 1) \div 31 = \\ = (89 + 3 + 1) \div 31 = \\ = 93 \div 31 = 3[/tex]
e)
[tex] = ( {2}^{8} + ( { {3}^{2} })^{2} + {5}^{6} + ( { {6}^{2} })^{2} ) \div (0 + ( { {2}^{2} })^{4} + \: {3}^{4 } + ( { {5}^{2} })^{3} + {6}^{4} ) = \\ = ( {2}^{8} + {3}^{2 \times 2} + {5}^{6} + {6}^{2 \times 2} ) \div (0 + {2}^{2 \times 4} + {3}^{4} + {5}^{2 \times 3} + {6}^{4} ) = \\ = ( {2}^{8} + {3}^{4} + {5}^{6} + {6}^{4} ) \div ( {2}^{8} + {3}^{4} + {5}^{6} + {6}^{4} ) = \\ = 1[/tex]
