Đáp án:
$a)
\dfrac{37}{7}\\
b)
\dfrac{-44}{5}\\
c)
648\\
d)
\dfrac{2}{3}\\$
Giải thích các bước giải:
$a)
5\dfrac{2}{7}.\dfrac{8}{11}+5\dfrac{2}{7}.\dfrac{5}{11}-5\dfrac{2}{7}.\dfrac{2}{11}\\
=5\dfrac{2}{7}.\left ( \dfrac{8}{11}+\dfrac{5}{11}-\dfrac{2}{11} \right )\\
=\dfrac{37}{7}.\dfrac{11}{11}=\dfrac{37}{7}\\
b)
2\dfrac{3}{4}.(-0,4)-1\dfrac{3}{5}.2,75+(-1,2):\dfrac{4}{11}\\
=\dfrac{11}{4}.\dfrac{-4}{10}-\dfrac{8}{5}.\dfrac{275}{100}+\dfrac{-12}{10}.\dfrac{11}{4}\\
=\dfrac{11}{4}.\dfrac{-2}{5}-\dfrac{8}{5}.\dfrac{11}{4}+\dfrac{-6}{5}.\dfrac{11}{4}\\
=\dfrac{11}{4}.\left ( \dfrac{-2}{5}-\dfrac{8}{5}+\dfrac{-6}{5} \right )\\
=\dfrac{11}{4}.\dfrac{-16}{5}\\
=\dfrac{-44}{5}\\
c)
\dfrac{5.27^3.4^5}{6^5}:\left ( \dfrac{5^5.2^4}{10^4}.\dfrac{2^6.3^4}{6^4} \right )\\
=\dfrac{5.(3^3)^3.(2^2)^5}{(2.3)^5}:\left ( \dfrac{5^5.2^4}{(2.5)^4}.\dfrac{2^6.3^4}{(2.3)^4} \right )\\
=\dfrac{5.3^9.2^{10}}{2^5.3^5}:\left ( \dfrac{5^5.2^4}{2^4.5^4}.\dfrac{2^6.3^4}{2^4.3^4} \right )\\
=\dfrac{5.3^4.2^5}{1}:\left ( \dfrac{5}{1}.\dfrac{2^2}{1} \right )\\
=5.3^4.2^5.\dfrac{1}{5.2^2}\\
=3^4.2^3=648\\
d)
\dfrac{5-\dfrac{5}{3}-\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}-\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}\\
=\dfrac{5\left (1-\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{27} \right )}{8\left (1-\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{27} \right )}:\dfrac{15\left (1-\dfrac{1}{11}+\dfrac{1}{121} \right )}{16\left (1-\dfrac{1}{11}+\dfrac{1}{121} \right )}\\
=\dfrac{5}{8}:\dfrac{15}{16}\\
=\dfrac{5}{8}.\dfrac{16}{15}\\
=\dfrac{2}{3}\\$
