Question

Сравнить числа: (0,71)^-5 и (2,13)^-5

Answer 1

$(0,71)^{-5}=( \frac{71}{100})^{-5}=( \frac{100}{71})^5\\\\(2,13)^{-5}=( \frac{213}{100})^{-5}=( \frac{100}{213})^5\\\\ \frac{100}{71}\ \textgreater \ 1\\\\ 0\ \textless \ \frac{100}{213}\ \textless \ 1 \\\\ \frac{100}{71}\ \textgreater \ \frac{100}{213}=\ \textgreater \ (\frac{100}{71})^5\ \textgreater \ (\frac{100}{213})^5=\ \textgreater \ (0,71)^{-5}\ \textgreater \ (2,13)^{-5}$