Задание 1.1

Question

1.1. Вычислите значение выражения:
\begin{enumerate}
\item $$3^{(\sqrt{2}+1)^{2}}: 3^{2 \sqrt{2}}$$
\item $$\left((3 \sqrt[3]{7})^{\sqrt{3}}\right)^{\sqrt{3}}$$
\item $$\sqrt[3]{6^{(\sqrt{5}+1)^{2}} \cdot 36^{-\sqrt{5}}} ;$$
\item $$\left(\left(\frac{1}{2}\right)^{\sqrt{2}}\right)^{-\sqrt{8}}$$.
\end{enumerate}

Gimli · Accepted Answer

\begin{enumerate}
\item $$3^{(\sqrt{2}+1)^{2}}: 3^{2 \sqrt{2}}=3^{2+2 \sqrt{2}+1}: 3^{2 \sqrt{2}}=3^{3+2 \sqrt{2}-2 \sqrt{2}}=3^{3}=27 ;$$
\item $$\left((3 \sqrt[3]{7})^{\sqrt{3}}\right)^{\sqrt{3}}=(3 \sqrt[3]{7})^{3}=3^{3} \cdot(\sqrt[3]{7})^{3}=27 \cdot 7=189;$$
\item $$\sqrt[3]{6^{(\sqrt{5}+1)^{2}} \cdot 36^{-\sqrt{5}}}=\sqrt[3]{6^{5+2 \sqrt{5}+1} \cdot 6^{-2 \sqrt{5}}}=\sqrt[3]{6^{6+2 \sqrt{5}-2 \sqrt{5}}}=\sqrt[3]{6^{6}}=6^{2}=36;$$
\item $$\left(\left(\frac{1}{2}\right)^{\sqrt{2}}\right)^{-\sqrt{8}}=\left(\frac{1}{2}\right)^{-\sqrt{16}}=\left(\frac{1}{2}\right)^{-4}=2^{4}=16$$
\end{enumerate}

Задание 1.1

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Задание 1.1

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