Question

Сравните: 1) и 2) и 3) и 4) и 5) и 6) и

Answer 1

$1) 2^{-5} \ \textless \ 2^{-4} \\2^{-5} = \frac{1}{2^5} \\2^{-4} = \frac{1}{2^4} \\ \frac{1}{2^5} \ \textless \ \frac{1}{2^4} \\ \\ 2) 7^{-5} \ \textless \ 7^{-3} \\7^{-5} = \frac{1}{7^5} \\7^{-3} = \frac{1}{7^3} \\ \frac{1}{7^5} \ \textless \ \frac{1}{7^3} \\ \\ 3)( -3)^{-3} = -3^{-3} \\ ( -3)^{-3}=\frac{1}{(-3)^3} = -\frac{1}{3^3} \\ -3^{-3}=-\frac{1}{3^3} \\ -\frac{1}{3^3} =-\frac{1}{3^3} \\ \\$

$4)(0,2)^{-3} \ \textgreater \ (0,5)^{-3} \\ (0,2)^{-3}= \frac{1}{0.2^3} = \frac{1}{ (\frac{2}{10} )^3} = \frac{1}{ \frac{2^3}{10^3}} = \frac{10^3}{2^3} =( \frac{10}{2} )^3=5^3 \\ (0,5)^{-3} = \frac{1}{0.5^3} = \frac{1}{ (\frac{5}{10} )^3} = \frac{1}{ \frac{5^3}{10^3}} = \frac{10^3}{5^3} =( \frac{10}{5} )^3=2^3 \\ 5^3\ \textgreater \ 2^3 \\$

$\\ (0,3)^{-3} \ \textless \ (0,3)^{-4} \\ 0.3^{-3}= \frac{1}{0.3^3}= \frac{1}{ \frac{3^4}{10^4} }= (\frac{10}{3})^3 \\ (0,3)^{-4} =\frac{1}{0.3^4}= \frac{1}{ \frac{3^4}{10^4} }= (\frac{10}{3})^4 \\ (\frac{10}{3})^3\ \textless \ (\frac{10}{3})^4$

$6)6^{-2} = (-6)^{-2} \\ 6^{-2}= \frac{1}{6^2} \\ (-6)^{-2}= \frac{1}{(-6)^2} = \frac{1}{6^2} \\ \frac{1}{6^2} = \frac{1}{6^2}$