Bài 1 trang 55 SGK Giải tích 12

Tính:

a) \({9^{{2 \over 5}}}{.27^{{2 \over 5}}}\);                       

b) \({144^{{3 \over 4}}}:{9^{{3 \over 4}}}\);

c) \({\left( {{1 \over {16}}} \right)^{ - 0,75}} + {\left( {0,25} \right)^{{{ - 5} \over 2}}}\);

d) \({\left( {0,04} \right)^{ - 1,5}} - {\left( {0,125} \right)^{{{ - 2} \over 3}}}\);

a) \({9^{{2 \over 5}}}{.27^{{2 \over 5}}} = {\left( {9.27} \right)^{{2 \over 5}}} = {\left( {{3^2}{{.3}^3}} \right)^{{2 \over 5}}} \) \(=\left( {{3^{5}}} \right)^{{2 \over 5}}=3^{5.{2 \over 5}} = {3^2} = 9\)

\( \eqalign{b) & {144^{{3 \over 4}}}:{9^{{3 \over 4}}} = \left( {144:9}\right)^{3 \over 4} = {\left( {{{\left( {{{12} \over 3}} \right)}^2}} \right)^{{3 \over 4}}} \cr & = \left( {{4^{2}}} \right)^{3 \over 4} =4^{2.{3 \over 4}}= {4^{{3 \over 2}}} = {2^3} = 8 \cr} \)

\( \eqalign{c)& {\left( {{1 \over {16}}} \right)^{ - 0,75}} + {\left( {0,25} \right)^{{{ - 5} \over 2}}} = {16^{0,75}} + {\left( {{1 \over 4}} \right)^{{{ - 5} \over 2}}} \cr & = {\left( {{2^4}} \right)^{0,75}} + {4^{2,5}} = {2^{4.0,75}} + {2^{2.2,5}} \cr & = {2^3} + {2^5} = 40 \cr} \)

\( \eqalign{d)& {\left( {0,04} \right)^{ - 1,5}} - {\left( {0,125} \right)^{{{ - 2} \over 3}}} \cr & = {\left( {{4 \over {100}}} \right)^{ - 1,5}} - {\left( {{{125} \over {1000}}} \right)^{{{ - 2} \over 3}}} \cr & = {\left( {{{100} \over 4}} \right)^{1,5}} - {8^{{2 \over 3}}} \cr & = {\left( {{5^2}} \right)^{{3 \over 2}}} - {\left( {{2^3}} \right)^{{2 \over 3}}} \cr & = {5^3} - {2^2} = 125 - 4 = 121 \cr} \)