Question

решить пример (0.008^-8)^2*(0.2^-23)^2

Answer 1

$\tt(0.008^{-8})^2\cdot(0.2^{-23})^2=(0.008)^{-16}\cdot(0.2)^{-46}=\bigg(\cfrac{8}{1000} \bigg)^{-16}\cdot\bigg(\cfrac{2}{10} \bigg)^{-46}=\\\\\\=\bigg(\cfrac{1000}{8} \bigg)^{16}\cdot\bigg(\cfrac{10}{2} \bigg)^{46}=125^{16}\cdot5^{46}=(5^3)^{16}\cdot5^{46}=5^{48}\cdot5^{46}=5^{94}$