Đề bài

Thực hiện các phép tính sau: a) \(\frac{{2{x^3}}}{{5{y^2}}}.\frac{{125{y^5}}}{{8x}}\); b) \(\frac{{24{y^5}}}{{7{x^2}}}.\left( { - \frac{{21x}}{{12{y^3}}}} \right)\)

Lời giải chi tiết

a) \(\frac{{2{x^3}}}{{5{y^2}}}.\frac{{125{y^5}}}{{8x}} = \frac{{2{x^3}.125{y^5}}}{{5{y^2}.8x}} = \frac{{{{2.5}^3}.x.{x^2}.{y^2}.{y^3}}}{{{{5.2}^3}.x.{y^2}}} = \frac{{25{x^2}{y^3}}}{4}\) b) \(\frac{{24{y^5}}}{{7{x^2}}}.\left( { - \frac{{21x}}{{12{y^3}}}} \right) = \frac{{24{y^5}.\left( { - 21x} \right)}}{{7{x^2}.12{y^3}}} = \frac{{ - {{3.2}^3}.3.7.{y^3}.{y^2}.x}}{{{{7.2}^2}.3.x.x.{y^3}}} = \frac{{ - 6{y^2}}}{x}\)