Tính:
a) \({\left( {\frac{1}{{256}}} \right)^{ - 0,75}} + {\left( {\frac{1}{{27}}} \right)^{ - \frac{4}{3}}}\)
b) \({\left( {\frac{1}{{49}}} \right)^{ - 1,5}} - {\left( {\frac{1}{{125}}} \right)^{ - \frac{2}{3}}}\)
c) \(\left( {{4^{3 + \sqrt 3 }} - {4^{\sqrt 3 - 1}}} \right){.2^{ - 2\sqrt 3 }}\)
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a) \({\left( {\frac{1}{{256}}} \right)^{ - 0,75}} + {\left( {\frac{1}{{27}}} \right)^{ - \frac{4}{3}}} = {\left( {\frac{1}{{256}}} \right)^{ - \frac{3}{4}}} + {\left( {\frac{1}{{27}}} \right)^{ - \frac{4}{3}}} = {256^{\frac{3}{4}}} + {27^{\frac{4}{3}}} = \sqrt[4]{{{{256}^3}}} + \sqrt[3]{{{{27}^4}}} = \sqrt[4]{{{{\left( {{2^8}} \right)}^3}}} + \sqrt[3]{{{{\left( {{3^3}} \right)}^4}}}\)
\( = \sqrt[4]{{{2^{24}}}} + \sqrt[3]{{{3^{12}}}} = {2^6} + {3^4} = 145\)
b)
${{\left( \frac{1}{49} \right)}^{-1,5}}-{{\left( \frac{1}{125} \right)}^{-\frac{2}{3}}}={{\left( \frac{1}{49} \right)}^{\frac{3}{2}}}-{{\left( \frac{1}{125} \right)}^{\frac{2}{3}}}={{\left( \frac{1}{7} \right)}^{2.\frac{-3}{2}}}\text{ }\!\!~\!\!\text{ }-{{\left( \frac{1}{5} \right)}^{3.\frac{-2}{3}}}$
$={{\left( {{7}^{-1}} \right)}^{-3}}-{{\left( {{5}^{-1}} \right)}^{-2}}={{7}^{3}}-{{5}^{2}}=318$
c) \(\left( {{4^{3 + \sqrt 3 }} - {4^{\sqrt 3 - 1}}} \right){.2^{ - 2\sqrt 3 }} = \left( {{2^{6 + 2\sqrt 3 }} - {2^{2\sqrt 3 - 2}}} \right){.2^{ - 2\sqrt 3 }} = {2^6} - {2^{ - 2}} = 64 - \frac{1}{4} = \frac{{255}}{4}\)