Bună!
a)
[tex]9 {}^{11} \times 3 {}^{31} \div 27 {}^{17} = \\ = 3 {}^{22} \times 3 {}^{31} \div 3 {}^{51} \\ = 3 {}^{2} = 9[/tex]
b)
[tex](2 {}^{2} \times 3) {}^{2} \div 6 + (2 \times5) {}^{3} + 45 {}^{45} \div 9 {}^{45} \div 5 {}^{44} - 2000 {}^{0} = \\ = \frac{(2 {}^{2} \times 3) {}^{2}}{6} + 10 {}^{3} + 5 {}^{45} \times \frac{1}{5 {}^{44} } - 1 \\ = \frac{2 {}^{4} \times 9 }{6} + 1000 + 5 - 1 \\ = \frac{2 {}^{4} \times 3}{2} + 1000 + 5 - 1 \\ = 2 {}^{3} \times 3 + 1000 + 5 - 1 \\ = 8 \times 3 + 1000 + 5 - 1 \\ = 24 + 1000 + 5 - 1 \\ = 1028[/tex]
c)
[tex]6 + 2 \times ((3 \times 5 {}^{2} - 2 {}^{2} \times 18 \div 3 {}^{2} + 3 \times 11) \div 2 {}^{2}) = \\ = 6 + 2 \times ((3 \times 25 - \frac{2 {}^{2} \times 18}{3 {}^{2} } + 33) \div 2 {}^{2}) \\ = 6 + 2 \times ((75 - \frac{4 \times 18}{9} + 33) \div 2 {}^{2}) \\ = 6 + 2 \times ((75 - 4 \times 2 + 33) \div 2 {}^{2}) \\ = 6 + 2 \times ((75 - 8 + 33) \div2 {}^{2}) \\ = 6 + 2 \times (100 \div 2 {}^{2}) \\ = 6 + 2 \times \frac{100}{2 {}^{2} } \\ = 6 + 2 \times \frac{100}{4} \\ = 6 + 2 \times 2 \\ = 6 + 50 \\ = 56[/tex]
d)
[tex](25 {}^{4} \times 5 {}^{6} \div 5 {}^{7}) {}^{3} \div 5 {}^{19} - (27 {}^{5} \times 9 {}^{2} \div 3 {}^{16}) {}^{3} \div 9 {}^{4} = \\ = (5 {}^{8}\times 5 {}^{6} \div 5 {}^{7}) {}^{3} \div 5 {}^{19} -(3 {}^{15} \times 3 {}^{4}\div 3 {}^{16}) {}^{3} \div 3 {}^{8} \\ = (5 {}^{7}) {}^{3} \div 5 {}^{19} - (3 {}^{3}) {}^{3} \div 3 {}^{8} \\ = 5 {}^{21}\div 5 {}^{19} -3 {}^{9} \div 3 {}^{8} \\ = 5 {}^{2} - 3 \\ = 25 - 3 =22[/tex]
e)
[tex](2 {}^{50} + 2 {}^{49} + 2 {}^{48}) \div (2 {}^{48} \times 7) \\ = (2 {}^{2} + 2 + 1) \times 2 {}^{48} \div (2 {}^{48} \times 7) \\ = (4+ 2 + 1) \times 2 {}^{48} \div (2 {}^{48} \times 7) \\ = 7\times 2 {}^{48} \div (2 {}^{48} \times 7) \\ = 1[/tex]
