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\(\left(\frac{-13}{21}\right)^2+\frac{13}{21}\cdot\frac{8}{21}\)
\(=\frac{169}{441}+\frac{104}{441}\)
\(=\frac{13}{21}\)
a,=\(\dfrac{8}{14}-\dfrac{1}{14}+\dfrac{5}{21}+\dfrac{3}{2}\)
=\(\dfrac{1}{2}+\dfrac{3}{2}+\dfrac{5}{21}\) =\(2+\dfrac{5}{21}\) =\(\dfrac{42}{21}+\dfrac{5}{21}\) =\(\dfrac{47}{21}\)
b,=\(\dfrac{11}{13}.\dfrac{12}{15}-\dfrac{7}{15}+\dfrac{14}{15}.\dfrac{11}{13}\)
=\(\dfrac{11}{13}.\left(\dfrac{12}{15}+\dfrac{14}{15}\right)-\dfrac{7}{15}\)
=\(\dfrac{11}{13}.\dfrac{26}{15}-\dfrac{17}{15}\) =\(\dfrac{22}{15}-\dfrac{17}{15}\) =\(\dfrac{5}{15}\) =\(\dfrac{1}{3}\)
c,=\(\left(\dfrac{3}{6}-\dfrac{2}{6}\right)^2\) =\(\left(\dfrac{1}{6}\right)^2\) =\(\dfrac{1}{36}\)
d,=câu này dễ mà
a,\(2^{31}=2^{30}.2=\left(2^3\right)^{10}.2=8^{10}.2< 9^{10}.3=\left(3^2\right)^{10}.3=3^{20}.3=3^{21}\)
b,\(2^{99}=\left(2^3\right)^{33}=8^{33}>3^{21}\)
c,\(31^{14}< 32^{14}=\left(2^5\right)^{14}=2^{70}< 2^{72}=\left(2^4\right)^{18}=16^{18}< 17^{18}\)
d,\(63^{10}< 64^{10}=\left(2^6\right)^{10}=2^{60}< 2^{65}=\left(2^5\right)^{13}=32^{13}< 33^{13}\)
\(=21\frac{13}{15}.\frac{-11}{5}+13\frac{2}{15}.\frac{-11}{5}\)\(+\frac{9}{16}\)
=\(\left(21\frac{13}{15}+13\frac{2}{15}\right).\frac{-11}{5}+\frac{9}{16}\)
\(=35.\frac{-11}{5}+\frac{9}{16}\)
\(=-77+\frac{9}{16}\)
\(=-77+1-\frac{7}{16}\)
\(=-77-\frac{7}{16}=-77\frac{7}{16}\)
Ta có:
\(21\frac{13}{15}.\frac{-11}{5}+13\frac{2}{15}:\frac{-5}{11}+\left(\frac{3}{4}\right)^2\)
\(=\frac{328}{15}.\frac{-11}{5}+\frac{197}{15}:\frac{-5}{11}+\frac{9}{16}\)
\(=\frac{328}{15}.\frac{-11}{5}+\frac{197}{15}.\frac{-11}{5}+\frac{9}{16}\)
\(=\frac{-5}{11}\left(\frac{328}{15}+\frac{197}{15}\right)+\frac{9}{16}\)
\(=\frac{-5}{11}.35+\frac{9}{16}\)
\(=\frac{-175}{11}+\frac{9}{16}\)
\(=\frac{-2701}{176}\)
Vậy........