Question

Найти значение выражения:

1.75^(1/9) * 4^(2/9) * 28^(8/9)

Answer 1

$1.75^{frac{1}{9}}*4^{frac{2}{9}}*28^{frac{8}{9}}=(1frac{75}{100})^{frac{1}{9}}*4^{frac{2}{9}}*(4*7)^{frac{8}{9}}=(1frac{3}{4})^{frac{1}{9}}*4^{frac{2}{9}}*4^{frac{8}{9}}*7^{frac{8}{9}}= \ =(frac{7}{4})^{frac{1}{9}}*4^{frac{8+2}{9}}*7^{frac{8}{9}}=frac{7^{frac{1}{9}}}{4^{frac{1}{9}}}*4^{frac{10}{9}}*7^{frac{8}{9}}=7^{frac{1}{9}}*4^{-frac{1}{9}}*4^{frac{10}{9}}*7^{frac{8}{9}}=\=7^{frac{1}{9}+frac{8}{9}}*4^{-frac{1}{9}+frac{10}{9}}=7^frac{9}{9}*4^frac{9}{9}=7^1*4^1=7*4=28$