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Question 1

Question 2

Решите задачу:

${6}^{ - 3} = \frac{1}{6 {}^{3} } \\ 5 {}^{ - 4} = \frac{1}{5 {}^{4} } \\ 4 {}^{ - 5} = \frac{1}{4 {}^{5} } \\ 3 {}^{ - 6} = \frac{1}{3 {}^{6} } \\ 2 {}^{ - 7} = \frac{1}{2 {}^{7} }$

$3 {}^{4} \times 3 {}^{2} = 3 {}^{4 + 2} = 3 {}^{6} \\ 3 {}^{4} \times 3 {}^{ - 2} = 3 {}^{4 + ( - 2)} = 3 {}^{4 + 2} = 3 {}^{6} \\ 3 {}^{ - 4} \times 3 {}^{2} = 3 {}^{ - 4 + 2} = 3 {}^{ - 2} = \frac{1}{3 {}^{2} } \\ 3 {}^{ - 4} \times 3 {}^{ - 2} = 3 {}^{ - 4 - 2} = 3 {}^{ - 6} \\ 5 {}^{4} \div {5}^{2} = 5 {}^{4 - 2} = 5 {}^{2} \\ 5 {}^{4} \div 5 {}^{ - 2} = 5 {}^{4 - ( - 2)} = 5 {}^{4 + 2} = 5 {}^{6} \\ 5 {}^{ - 4} \div 5 {}^{ 2} = 5 {}^{ - 4 - 2} = 5 {}^{ - 6} = \frac{1}{5 {}^{6} } \\ 5 {}^{ - 4} \div 5 {}^{ - 2} = 5 { }^{- 4 - ( - 2)} = {5}^{ - 4 + 2} = {5}^{ - 2} = \frac{1}{5 {}^{2} } \\ (7 {}^{2} ) {}^{3} = 7 {}^{2 \times 3} = 7 {}^{6} \\ (7 {}^{2} ) {}^{3} = 7 {}^{ - 2 \times 3} = 7 {}^{ - 6} \\ (7 {}^{2} ) {}^{ - 3} = 7 {}^{2 \times( - 3)} = 7 {}^{ - 6} \\ (7 {}^{ - 2} ) {}^{ - 3} = 7 {}^{ - 2 \times ( - 3)} = 7 {}^{6}$

$(1.25) {}^{3} \times 8 {}^{3} = (1.25 \times 8) {}^{3} = 10 {}^{3} = 1000 \\ (0.25) {}^{5} \times 4 {}^{5} = (0.25 \times 4) {}^{5} = 1 {}^{5} = 1 \\ (0.125) {}^{100} \times 8 {}^{100} = (0.125 \times 8) {}^{100} = 1 {}^{100} = 1 \\ 25 {}^{2017} \times ( - 0.04) {}^{2017} = ( - 0.04 \times 25) {}^{2017} = ( - 1) {}^{2017} = - 1$

$(0.8) {}^{ - 3} \times (12.5) {}^{ - 3} = (0.8 \times 12.5) {}^{ - 3} = 10 {}^{ - 3} = \frac{1}{10 {}^{3} } = \frac{1}{1000} = 0.001 \\ (2.5) {}^{ - 3} \times (0.4) {}^{ - 3} = (2.5 \times 0.4) {}^{ - 3} = 1 {}^{ - 3} = \frac{1}{1 {}^{3} } = \frac{1}{1} = 1 \\ 100 {}^{ - 4} \times ( - 0.001) {}^{ - 4} = ( - 0.001 \times 100) {}^{ - 4} = ( - 0.1) {}^{ - 4} = (- \frac{1}{10} ) {}^{ - 4} = ( - \frac{10}{1} ) {}^{4} = 10000$

$\frac{25 {}^{ - 3} }{(12.5) {}^{ - 3} } = ( \frac{25}{12.5} ) {}^{ - 3} = ( \frac{2}{1} ) {}^{ - 3} = ( \frac{1}{2} ) {}^{3} = \frac{1 {}^{3} }{2 {}^{3} } = \frac{1}{8} = 0.125 \\ \frac{(13.5) { }^{ - 3} }{27 {}^{ - 3} } = ( \frac{13.5}{27} ) {}^{ - 3} = ( \frac{1}{2} ) {}^{ - 3} = (\frac{2}{1} ) {}^{3} = 2 {}^{3} = 8$