Răspuns:
[tex]a) \: (7 {}^{4}) {}^{5} \times {7}^{18} = {7}^{(4 \times 5)} \times {7}^{18} \\ = 7 {}^{20} \times {7}^{18} = 7 {}^{20 + 18} = {7}^{38} [/tex]
[tex]b) \: 13 {}^{30} \times (13 {}^{4} ) {}^{6} = 13 {}^{30} \times {13}^{(4 \times 6)} \\ = 13 {}^{30} \times {13}^{24} = {13}^{30 + 24} = 13 {}^{54 } [/tex]
[tex]c) \: (2 {}^{11} ) {}^{20} \div 2 {}^{200} = 2 {}^{(11 \times 20)} \div 2 {}^{200} \\ = 2 {}^{220} \div 2 {}^{200} = 2 {}^{220 - 200} = 2 {}^{20} [/tex]
[tex]d) \: (15 {}^{8} ) {}^{21} \div (15 {}^{7} ) {}^{24} = 15 {}^{(8 \times 21)} \div 15 {}^{(7 \times 24)} \\ = 15 {}^{168} \div 15 {}^{168} = 15 {}^{168 \div 168} = 15 {}^{0} = 1[/tex]
[tex]e) \: (3 {}^{5} ) {}^{7} \times ( 3 {}^{8} ) {}^{4} = 3 {}^{(5 \times 7)} \times 3 {}^{(8 \times 4)} \\ = 3 {}^{35} \times 3 {}^{32} = 3 {}^{35 + 32} = 3 {}^{67} [/tex]
[tex]f) \: (2 {}^{6} ) {}^{4} \times (2 {}^{5} ) {}^{3} \div (2 {}^{3} ) {}^{12} = 2 {}^{(6 \times 4)} \times 2 {}^{(5 \times 3)} \div 2 {}^{(3 \times 12)} \\ = 2 {}^{24} \times 2 {}^{15} \div2 {}^{36} = 2 {}^{24 + 15} \div 2 {}^{36} \\ = 2 {}^{39} \div 2 {}^{36} = 2 {}^{39 - 36} = 2 {}^{3} = 8[/tex]
