Задание 1.2

Question

Найдите значение выражения:
\begin{enumerate}
\item $$5^{(\sqrt{3}-1)^{2}}:\left(\frac{1}{5}\right)^{2 \sqrt{3}} ;$$
\item $$\left((\sqrt{2})^{\sqrt{6}}\right)^{\sqrt{6}}$$
\item $$\left((\sqrt[5]{10})^{\sqrt{5}}\right)^{-2 \sqrt{5}}$$
\end{enumerate}

Gimli · Accepted Answer

\begin{enumerate}
\item $$5^{(\sqrt{3}-1)^{2}}:\left(\frac{1}{5}\right)^{2 \sqrt{3}}=5^{3-2 \sqrt{3}+1} \cdot 5^{2 \sqrt{3}}=5^{4-2 \sqrt{3}+2 \sqrt{3}}=5^{4}=625$$
\item $$\left((\sqrt{2})^{\sqrt{6}}\right)^{\sqrt{6}}=(\sqrt{2})^{6}=\left((\sqrt{2})^{2}\right)^{3}=2^{3}=8$$
\item $$\left((\sqrt[5]{10})^{\sqrt{5}}\right)^{-2 \sqrt{5}}=(\sqrt[5]{10})^{-10}=10^{\frac{1}{5} \cdot(-10)}=10^{-2}=0,01$$
\end{enumerate}

Задание 1.2

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Задание 1.2

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