Rút gọn biểu thức ( 7/ 2 mũ 9 – 14/2 mũ 11+21/768)mũ 2 : ( 5/2 mũ 9 – 20/2 mũ 12 + 25/1280) mũ 2 23/07/2021 Bởi Parker Rút gọn biểu thức ( 7/ 2 mũ 9 – 14/2 mũ 11+21/768)mũ 2 : ( 5/2 mũ 9 – 20/2 mũ 12 + 25/1280) mũ 2
Đáp án: $\begin{array}{l}{\left( {\dfrac{7}{{{2^9}}} – \dfrac{{14}}{{{2^{11}}}} + \dfrac{{21}}{{768}}} \right)^2}:{\left( {\dfrac{5}{{{2^9}}} – \dfrac{{20}}{{{2^{12}}}} + \dfrac{{25}}{{1280}}} \right)^2}\\ = {\left( {\dfrac{7}{{{2^9}}} – \dfrac{7}{{{2^{10}}}} + \dfrac{7}{{256}}} \right)^2}:{\left( {\dfrac{5}{{{2^9}}} – \dfrac{5}{{{2^{10}}}} + \dfrac{5}{{256}}} \right)^2}\\ = {7^2}.{\left( {\dfrac{1}{{{2^9}}} – \dfrac{1}{{{2^{10}}}} + \dfrac{1}{{256}}} \right)^2}:\left[ {{5^2}.{{\left( {\dfrac{1}{{{2^9}}} – \dfrac{1}{{{2^{10}}}} + \dfrac{1}{{256}}} \right)}^2}} \right]\\ = {7^2}:{5^2}\\ = \dfrac{{49}}{{25}}\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
{\left( {\dfrac{7}{{{2^9}}} – \dfrac{{14}}{{{2^{11}}}} + \dfrac{{21}}{{768}}} \right)^2}:{\left( {\dfrac{5}{{{2^9}}} – \dfrac{{20}}{{{2^{12}}}} + \dfrac{{25}}{{1280}}} \right)^2}\\
= {\left( {\dfrac{7}{{{2^9}}} – \dfrac{7}{{{2^{10}}}} + \dfrac{7}{{256}}} \right)^2}:{\left( {\dfrac{5}{{{2^9}}} – \dfrac{5}{{{2^{10}}}} + \dfrac{5}{{256}}} \right)^2}\\
= {7^2}.{\left( {\dfrac{1}{{{2^9}}} – \dfrac{1}{{{2^{10}}}} + \dfrac{1}{{256}}} \right)^2}:\left[ {{5^2}.{{\left( {\dfrac{1}{{{2^9}}} – \dfrac{1}{{{2^{10}}}} + \dfrac{1}{{256}}} \right)}^2}} \right]\\
= {7^2}:{5^2}\\
= \dfrac{{49}}{{25}}
\end{array}$