by Thực hiện các phép tính: \(\,\frac{{{2^{10}}{{.9}^{41}}{{.25}^{23}}}}{{{3^{50}}{{.15}^{35}}{{.10}^9}}}\)
A. \(\frac{{23}}{9}\)
B. \(\frac{{5}}{9}\)
C. \(\frac{{37}}{9}\)
D. \(\frac{{50}}{9}\)
Hướng dẫn
Chọn đáp án là: D
Phương pháp giải:
Đưa các lũy thừa về cùng cơ số rồi rút gọn.
\(\begin{array}{l}\,\frac{{{2^{10}}{{.9}^{41}}{{.25}^{23}}}}{{{3^{50}}{{.15}^{35}}{{.10}^9}}} = \frac{{{2^{10}}.{{\left( {{3^2}} \right)}^{41}}.{{\left( {{5^2}} \right)}^{23}}}}{{{3^{50}}.{{\left( {3.5} \right)}^{35}}.{{\left( {2.5} \right)}^9}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{2^{10}}{{.3}^{82}}{{.5}^{46}}}}{{{3^{50}}{{.3}^{35}}{{.5}^{35}}{{.2}^9}{{.5}^9}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{2^{10}}{{.3}^{82}}{{.5}^{46}}}}{{{3^{85}}{{.5}^{44}}{{.2}^9}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{{2.1.5}^2}}}{{{3^2}.1.1}} = \frac{{50}}{9}\end{array}\)
Chọn D
