Question

Упростите выражение
$( a^{1+ sqrt{5} }) ^{ sqrt{5}+1 }* frac{1}{a^{6}+ sqrt{5} }$

Answer 1

$(a^{1+sqrt5})^{sqrt5+1}cdot frac{1}{a^{6+sqrt5}}=a^{(1+sqrt5)^2}cdot frac{1}{a^{6+sqrt5}}=frac{a^{6+2sqrt5}}{a^{6+sqrt5}}=\\=frac{a^{6+sqrt5}cdot a^{sqrt5}}{a^{6+sqrt5}}=a^{sqrt5}\\(1+sqrt5)^2=1+2sqrt5+5=6+2sqrt5=(6+sqrt5)+sqrt5$b