Đề bài
Tính
a]\[{\left[ {\dfrac{3}{7} + \dfrac{1}{2}} \right]^2}\]
b] \[{\left[ {\dfrac{3}{4} - \dfrac{5}{6}} \right]^2}\]
c] \[\dfrac{{{5^4}{{.20}^4}}}{{{{25}^5}{{.4}^5}}}\]
d] \[{\left[ {\dfrac{{ - 10}}{3}} \right]^5}.{\left[ {\dfrac{{ - 6}}{5}} \right]^4}\]
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Ta sử dụng các công thức sau:
\[{\left[ {x.y} \right]^n} = {x^n}.{y^n}\]
\[{x^n} = \underbrace {x.x.x...x}_{n\,\,\,thừa\,\,số}\left[ {x \in Q,n \in N,n > 1} \right]\]
\[{\left[ {\dfrac{x}{y}} \right]^n} = \dfrac{{{x^n}}}{{{y^n}}}\,\,\left[ {y \ne 0} \right]\]
Lời giải chi tiết
a]\[{\left[ {\dfrac{3}{7} + \dfrac{1}{2}} \right]^2} = {\left[ {\dfrac{6}{{14}} + \dfrac{7}{{14}}} \right]^2} \]\[\,= {\left[ {\dfrac{{13}}{{14}}} \right]^2}= \dfrac{{169}}{{196}}\]
b] \[{\left[ {\dfrac{3}{4} - \dfrac{5}{6}} \right]^2} = {\left[ {\dfrac{9}{{12}} - \dfrac{{10}}{{12}}} \right]^2}\]\[\, = {\left[ {\dfrac{{ - 1}}{{12}}} \right]^2} = \dfrac{1}{{144}}\]
c] \[\dfrac{{{5^4}{{.20}^4}}}{{{{25}^5}{{.4}^5}}} = \dfrac{{{{\left[ {5.20} \right]}^4}}}{{{{\left[ {25.4} \right]}^5}}} = \dfrac{{{{100}^4}}}{{{{100}^5}}} = \dfrac{1}{{100}}\]
d]
\[\begin{array}{l}
{\left[ {\dfrac{{ - 10}}{3}} \right]^5}.{\left[ {\dfrac{{ - 6}}{5}} \right]^4}\\
= \left[ {\dfrac{{ - 10}}{3}} \right].{\left[ {\dfrac{{ - 10}}{3}} \right]^4}.{\left[ {\dfrac{{ - 6}}{5}} \right]^4}\\
= \dfrac{{ - 10}}{3}.{\left[ {\left[ {\dfrac{{ - 10}}{3}} \right].\left[ {\dfrac{{ - 6}}{5}} \right]} \right]^4}\\
= \dfrac{{ - 10}}{3}.{\left[ {\dfrac{{ - 10.\left[ { - 6} \right]}}{{3.5}}} \right]^4}\\
= \dfrac{{ - 10}}{3}.{\left[ {\dfrac{{60}}{{15}}} \right]^4}\\
= \dfrac{{ - 10}}{3}{.4^4}\\
= \dfrac{{ - 10}}{3}.256 = \dfrac{{ - 2560}}{3}
\end{array}\]
Cách khác câu d:
\[{\left[ {\dfrac{{ - 10}}{3}} \right]^5}.{\left[ {\dfrac{{ - 6}}{5}} \right]^4} \]\[ = \dfrac{{{{\left[ { - 10} \right]}^5}}}{{{3^5}}}.\dfrac{{{{\left[ { - 6} \right]}^4}}}{{{5^4}}}\]\[\,= \dfrac{{{{\left[ { - 2.5} \right]}^5}}}{{{3^5}}}.\dfrac{{{{\left[ { - 2.3} \right]}^4}}}{{{5^4}}} \]\[ = \dfrac{{{{\left[ { - 2} \right]}^5}{{.5}^5}}}{{{3^5}}}.\dfrac{{{{\left[ { - 2} \right]}^4}{{.3}^4}}}{{{5^4}}}\]\[= \dfrac{{ {[-2]^5}{{.5}^5}.{{[-2]}^4}{{.3}^4}}}{{{3^5}{{.5}^4}}} = \dfrac{{ {{5.[-2]}^9}}}{3} = - \dfrac{{2560}}{3}\]