31/29

\(=\frac{-\frac{1}{8}-\frac{27}{64}.4}{-2+\frac{9}{16}-\frac{3}{8}}\)

\(=\frac{-\frac{1}{8}-\frac{27}{16.4}.4}{-2+\frac{9-6}{16}}\)

\(=\frac{-\frac{1}{8}-\frac{27}{16}}{-2+\frac{3}{16}}\)

\(=\frac{-\left(\frac{2+27}{16}\right)}{\frac{-32+3}{16}}\)

\(=\frac{-\frac{29}{16}}{\frac{-29}{16}}\)

\(=1\)

$\textbf{A}$

$A=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{(2^2\cdot3)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{(125\cdot7)^3+5^9\cdot14^3}$

$=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+2^3\cdot5^9\cdot7^3}$

$=\dfrac{2^{12}\cdot3^4(3-1)}{2^{12}\cdot3^5(3+1)}-\dfrac{5^{10}\cdot7^3(1-7)}{5^9\cdot7^3(1+8)}$

$=\dfrac{2}{12}-\dfrac{-30}{9}$

$=\dfrac16+\dfrac{10}{3}$

$=\boxed{\dfrac72}.$

$\textbf{B}$

$B=\dfrac{\left(-\dfrac12\right)^3-\left(\dfrac34\right)^3\cdot(-2)^2}{2\cdot(-1)^5+\left(\dfrac34\right)^2-\dfrac38}$

$=\dfrac{-\dfrac18-\dfrac{27}{64}\cdot4}{-2+\dfrac9{16}-\dfrac38}$

$=\dfrac{-\dfrac18-\dfrac{27}{16}}{-2+\dfrac3{16}}$

$=\dfrac{-\dfrac{29}{16}}{-\dfrac{29}{16}}$

$=\boxed{1}.$

\(P=\left(-0,5-\frac{3}{5}\right):\left(-3\right)+\frac{1}{3}-\left(-\frac{1}{6}\right):\left(-2\right)\)

\(P=\left(-1,1\right):\left(-3\right)+\frac{1}{3}+\frac{1}{6}:\left(-2\right)\)

\(P=\frac{11}{30}+\frac{1}{3}+\left(-\frac{1}{12}\right)\)

\(P=\frac{37}{60}\)

\(Q=\left(\frac{2}{25}-1,008\right):\frac{4}{7}:\left[\left(3\frac{1}{4}-6\frac{5}{9}\right).2\frac{2}{17}\right]\)

\(Q=\left(-0,928\right):\frac{4}{7}:\left[\left(-\frac{119}{36}\right).2\frac{2}{17}\right]\)

\(Q=\left(-1,624\right):\left(-\frac{245}{36}\right)\)

\(Q=\frac{1044}{4375}\)

\(a,\left[\left(-\frac{1}{2}\right)^3-\left(\frac{3}{4}\right)^3.\left(-2\right)^2\right]:\left[2.\left(-1\right)^5+\left(\frac{3}{4}\right)^2-\frac{3}{8}\right]\)

\(=\left[\left(-\frac{1}{8}\right)-\frac{27}{64}.4\right]:\left[2.\left(-1\right)+\frac{9}{16}-\frac{3}{8}\right]\)

\(=\left[\left(-\frac{1}{8}-\frac{27}{16}\right)\right]:\left[-2+\frac{9}{16}-\frac{3}{8}\right]\)

\(=\frac{-2-27}{16}:\frac{-32+9-6}{16}\)

\(=-\frac{29}{16}:\frac{-29}{16}=1\)

\(b,\left[\left(\frac{4}{3}\right)^{-2}\left(\frac{3}{2}\right)^4\right]:\left(\frac{3}{2}\right)^6\)

\(=\left(\frac{9}{16}.\frac{81}{16}\right):\frac{729}{64}\)

\(=\frac{729}{64}:\frac{729}{64}=1\)

Biểu thức 1

$3\dfrac12\cdot\dfrac4{49}-\left(2,(4)\cdot2\dfrac5{11}\right):\left(-\dfrac{42}{8}\right)$

$=\dfrac72\cdot\dfrac4{49}-\left(\dfrac{22}{9}\cdot\dfrac{27}{11}\right)\cdot\left(-\dfrac4{21}\right)$

$=\dfrac27-6\cdot\left(-\dfrac4{21}\right)$

$=\dfrac27+\dfrac87$

$=\dfrac{10}{7}.$

Biểu thức 2

$\left[0,(5)\cdot0,(2)\right]:\left(3\dfrac13:\dfrac{33}{25}\right)-\left(\dfrac25\cdot3\dfrac13\right):\dfrac43$

$=\left(\dfrac59\cdot\dfrac29\right):\left(\dfrac{10}{3}:\dfrac{33}{25}\right)-\left(\dfrac25\cdot\dfrac{10}{3}\right):\dfrac43$

$=\dfrac{10}{81}:\dfrac{250}{99}-\dfrac43\cdot\dfrac34$

$=\dfrac{10}{81}\cdot\dfrac{99}{250}-1$

$=\dfrac{11}{225}-1$

$=-\dfrac{214}{225}.$