Question

Упростите выражения:

Answer 1

$1)\; \; \sqrt{a\sqrt{a}}=\sqrt{\sqrt{a^3}}=\sqrt[4]{a^3}\\\\\\2)\; \; a^8(a^{-2}-a^{-4})(a^4+a^5)^{-1}=a^8\, (\frac{1}{a^2}-\frac{1}{a^4})\cdot \frac{1}{a^4+a^5}=\\\\=\frac{a^2-1}{a^4}\cdot \frac{a^8}{a^4(1+a)}=\frac{(a-1)(a+1)}{a+1}=a-1\\\\\\3)\; \; (y^{\frac{5}{7} })^{1,4}\cdot (y^{-\frac{3}{8}})^{2,4}=y^{\frac{5}{7}\cdot \frac{14}{10}}\cdot y^{-\frac{3}{8}\cdot \frac{24}{10}}=y^1\cdot y^{-\frac{9}{10}}=y^{\frac{1}{10}}$