Nội dung bài giảng
Hãy tính
a) \({\left( {{{\left( {\sqrt 3 } \right)}^{\sqrt 3 }}} \right)^{\sqrt 3 }}\) b) \({4^{1 - 2\sqrt 3 }}{.16^{1 + \sqrt 3 }}\)
c)\({27^{\sqrt 2 }}:{3^{3\sqrt 2 }}\) d) \({\left( {{2^{\root 5 \of 8 }}} \right)^{\root 5 \of 4 }}\)
Giải
a) \({\left( {{{\left( {\sqrt 3 } \right)}^{\sqrt 3 }}} \right)^{\sqrt 3 }}={\left( {\sqrt 3 } \right)^3} = 3\sqrt 3 \)
b) \({4^{1 - 2\sqrt 3 }}{.16^{1 + \sqrt 3 }}= {4^{1 - 2\sqrt 3 }}{.4^{2\left( {1 + \sqrt 3 } \right)}}\)
\(= {4^{1 - 2\sqrt 3 + 2 + 2\sqrt 3 }} = {4^3} = 64\)
c) \({27^{\sqrt 2 }}:{3^{3\sqrt 2 }}={3^{3\sqrt 2 }}:{3^{3\sqrt 2 }} = 1\)
d) \({\left( {{2^{\root 5 \of 8 }}} \right)^{\root 5 \of 4 }}={2^{\root 5 \of 8 .\root 5 \of 4 }} = {2^{\root 5 \of {32} }} = {2^2} = 4\)