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Thực hiện các phép tính sau:
a) \(2y:{{4x} \over {5xy}}.{{64xy} \over {100{x^3}{y^4}}}\) ;
b) \({{6df} \over {9{f^3}}}.{{3f} \over {16{d^2}}}.{{8{d^3}{f^2}} \over {27d}}\) ;
c) \({{3ps} \over {4pqr}}:{{3p{q^2}} \over {12{p^3}q}}.{{14{s^3}} \over {7qr}}\) ;
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d) \({{3w – 7} \over {5{w^3}}}:{{21 – 9w} \over {27w}}\) .
\(\eqalign{ & a)\,\,2y:{{4x} \over {5xy}}.{{64xy} \over {100{x^3}{y^4}}} = 2y.{{5xy} \over {4x}}.{{64xy} \over {100{x^3}{y^4}}} \cr & = 2y.{{5y} \over 4}.{{16} \over {25{x^2}{y^3}}} = {{2y.5y.16} \over {4.25{x^2}{y^3}}} = {{160{y^2}} \over {100{x^2}{y^3}}} = {8 \over {5{x^2}y}} \cr & b)\,\,{{6df} \over {9{f^3}}}.{{3f} \over {16{d^2}}}:{{8{d^3}{f^2}} \over {27d}} = {{6df} \over {9{f^3}}}.{{3f} \over {16{d^2}}}.{{27d} \over {8{d^3}{f^2}}} \cr & = {{162df} \over {384{d^4}{f^4}}} = {{27} \over {64{d^3}{f^3}}} \cr & c)\,\,{{3w – 7} \over {5{w^3}}}:{{21 – 9w} \over {27w}} = {{3w – 7} \over {5{w^3}}}.{{27w} \over {21 – 9w}} \cr & = {{\left( {3w – 7} \right).27w} \over {5{w^3}\left( {21 – 9w} \right)}} = {{ – \left( {7 – 3w} \right).27w} \over {5{w^3}.3\left( {7w – 3} \right)}} = {{ – 9} \over {5{w^2}}} \cr} \)