Question

Найти значение выражения

Answer 1

$\displaystyle\bf\\1)\\\\5^{(\sqrt{3}-1)^{2} } :\Big(\frac{1}{5} \Big)^{2\sqrt{3} } =5^{3-2\sqrt{3}+1 } :5^{-2\sqrt{3} } =5^{4-2\sqrt{3} -(-2\sqrt{3} )} =\\\\\\=5^{4-2\sqrt{3} +2\sqrt{3} } =5^{4} =625\\\\\\2)\\\\\Big((\sqrt{2} )^{\sqrt{6} } \Big)^{\sqrt{6} } =\Big(\sqrt{2} \Big)^{\sqrt{6}\cdot\sqrt{6} } =\Big(\sqrt{2}\Big)^{6} =8\\\\\\3)$

$\displaystyle\bf\\\Big((\sqrt[5]{10} )^{\sqrt5} } \Big)^{-2\sqrt{5} } =\Big(\sqrt[5]{10}\Big)^{\sqrt{5} \cdot(-2\sqrt{5}) } =\Big(\sqrt[5]{10} \Big)^{-10} =\Big(10^{\frac{1}{5} }\Big)^{-10} =\\\\\\=10^{-2}=0,01$