Tính các biểu thức: \({\left( {0,{5^{\sqrt 2 }}} \right)^{\sqrt 8 }}\); \({2^{2 - 3\sqrt 5 }}{.8^{\sqrt 5 }}\); \({3^{1 + 2\root 3 \of 2 }}:{9^{\root 3 \of 2 }}\).
2 câu trả lời
$$\eqalign{ & {\left( {0,{5^{\sqrt 2 }}} \right)^{\sqrt 8 }} = 0,{5^{\sqrt 2 .\sqrt 8 }} = 0,{5^{\sqrt {16} }} = 0,{5^4} = {\left( {{1 \over 2}} \right)^4} = {1 \over {16}} \cr & {2^{2 - 3\sqrt 5 }}{.8^{\sqrt 5 }} = {2^{2 - 3\sqrt 5 }}.{\left( {{2^3}} \right)^{\sqrt 5 }} = {2^{2 - 3\sqrt 5 }}{.2^{3\sqrt 5 }} = {2^{2 - 3\sqrt 5 + 3\sqrt 5 }} = {2^2} = 4 \cr & {3^{1 + 2\root 3 \of 2 }}:{9^{\root 3 \of 2 }} = {3^{1 + 2\root 3 \of 2 }}:{3^{2\root 3 \of 2 }} = {3^{1 + 2\root 3 \of 2 - 2\root 3 \of 2 }} = {3^1} = 3 \cr} $$
\[\begin{array}{l} {\left( {0,{5^{\sqrt 2 }}} \right)^{\sqrt 8 }} = 0,{5^{\sqrt 2 .\sqrt 8 }} = 0,{5^{\sqrt {16} }} = 0,{5^4} = {\left( {\frac{1}{2}} \right)^4} = \frac{1}{{16}}.\\ {2^{2 - 3\sqrt 5 }}{.8^{\sqrt 5 }} = {2^{2 - 3\sqrt 5 }}.{\left( {{2^3}} \right)^{\sqrt 5 }} = {2^{2 - 3\sqrt 5 }}{.2^{3\sqrt 5 }} = {2^{2 - 3\sqrt 5 + 3\sqrt 5 }} = {2^2} = 4.\\ {3^{1 + 2\sqrt[3]{2}}}:{9^{\sqrt[3]{2}}} = {3^{1 + 2\sqrt[3]{2}}}:{3^{2\sqrt[3]{2}}} = {3^{1 + 2\sqrt[3]{2} - 2\sqrt[3]{2}}} = 3. \end{array}\]
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