Question

Спростіть вираз з фото:

Answer 1

Объяснение:

$\displaystyle\\(\frac{a^{-\frac{3}{4}}*a^{\frac{1}{2}} }{a^{\frac{5}{12}}}*\frac{a^{\frac{5}{6}} }{a^{-\frac{1}{6} }} } )^3=(\frac{a^{-\frac{3}{4}+\frac{1}{2}} }{a^{\frac{5}{12}} } *a^{\frac{5}{6}-(-\frac{1}{6} )})^3=(\frac{a^{\frac{-1+2*1}{4} }}{a^{\frac{5}{12} }} *a^{\frac{5}{6}+\frac{1}{6} })^3=\\\\.$$\displaystyle\\=(\frac{a^{-\frac{1}{4}} }{a^{\frac{5}{12}} }*a)^3=(a^{-\frac{1}{4}-\frac{5}{12}}*a)^3=(a^{-\frac{1*3+5*1}{12}}*a)^3=(a^{-\frac{3+5}{12} *}*a)^3=\\\\\\ =(a^{-\frac{2}{3}}* a^1)^3=(a^{-\frac{2}{3}+1})^3=(a^{\frac{1}{3}})^3= a.$