Bài 103845

Question

Tính biểu thức : $A = {\left\{ {\left[ {{3^{\frac{3}{2}}}{{.5}^{\frac{5}{3}}}:{2^{\frac{7}{4}}}} \right]:\left[ {16:\left( {{5^{\frac{1}{3}}}{{.2}^{\frac{1}{4}}}{{.3}^{\frac{1}{2}}}} \right)} \right]} \right\}^{\frac{1}{2}}}$

score 0 · Answer 1

Đặt : $B = {3^{\frac{3}{2}}}{.5^{\frac{5}{3}}}{.2^{\frac{7}{4}}} = \sqrt {{3^3}} .\sqrt[3]{{{5^5}}}:\frac{1}{{\sqrt[4]{{{2^7}}}}}$
$ = 3\sqrt 3 .5\sqrt[3]{{25}}:\frac{1}{{2\sqrt[4]{8}}} = 30\sqrt 3 .\sqrt[3]{{25}}.\sqrt[4]{8}$
$C$ $ = 16:\left( {{5^{\frac{1}{3}}}{{.2}^{\frac{1}{4}}}{{.3}^{\frac{1}{2}}}} \right) = 16:\left( {\sqrt[3]{5}.\sqrt[4]{2}.\sqrt 3 } \right) = \frac{{16}}{{\sqrt 3 .\sqrt[4]{2}.\sqrt[3]{5}}}$
$ \Rightarrow A = {\left( {\frac{B}{C}} \right)^{\frac{1}{2}}} = {\left( {\frac{{30\sqrt 3 .\sqrt[3]{{25}}.\sqrt[4]{8}}}{{16}} \times \sqrt 3 .\sqrt[3]{5}.\sqrt[4]{2}} \right)^{\frac{1}{2}}} = {\left( {\frac{{90.\sqrt[3]{{{5^3}.\sqrt[4]{{{2^4}}}}}}}{{16}}} \right)^{\frac{1}{2}}} = \frac{{15}}{2}$

Bài 103845

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Bài 103845

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