1: \(-12:\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
\(=-12:\left(\dfrac{9}{12}-\dfrac{10}{12}\right)^2\)
\(=-12:\left(-\dfrac{1}{12}\right)^2\)
\(=-12:\dfrac{1}{144}=-12\cdot144=-1728\)
2: \(\left(\dfrac{1}{3}-2\dfrac{1}{6}\right)^2:\left(-3\dfrac{13}{36}\right)\)
\(=\left(\dfrac{1}{3}-\dfrac{13}{6}\right)^2:\dfrac{-119}{36}\)
\(=\left(\dfrac{2}{6}-\dfrac{13}{6}\right)^2\cdot\dfrac{36}{-119}\)
\(=\dfrac{121}{36}\cdot\dfrac{36}{-119}=\dfrac{-121}{119}\)
3: \(2^3+3\cdot\left(\dfrac{1}{9}\right)^0-\dfrac{1}{2^2}\cdot4+\left[\left(-2\right)^2:\dfrac{1}{2}\right]\cdot8\)
\(=8+3-\dfrac{1}{4}\cdot4+\left[4\cdot2\right]\cdot8\)
=11-1+64
=74
4: \(\left|-\dfrac{1}{2}\right|+\left(-\dfrac{1}{2}\right)^2:\left|-2\right|-\left(-\dfrac{2}{3}\right)^0\)
\(=\dfrac{1}{2}+\dfrac{1}{4}:2-1\)
\(=-\dfrac{1}{2}+\dfrac{1}{8}=-\dfrac{3}{8}\)
5: \(-\sqrt{64}+2\cdot\sqrt{\left(-5\right)^2}-7\cdot\sqrt{0,01}+8\cdot\sqrt{\dfrac{25}{16}}\)
\(=-8+2\cdot5-7\cdot0,1+8\cdot\dfrac{5}{4}\)
\(=2-0,7+10\)
=12-0,7
=11,3
6: \(\left[3\sqrt{225}-5\sqrt{\left(-12\right)^2}-12\cdot\left|-\dfrac{7}{6}\right|\right]\cdot\sqrt{2\dfrac{1}{4}}\)
\(=\left[3\cdot15-5\cdot12-12\cdot\dfrac{7}{6}\right]\cdot\sqrt{\dfrac{9}{4}}\)
\(=\left[45-60-14\right]\cdot\dfrac{3}{2}\)
\(=-29\cdot\dfrac{3}{2}=-\dfrac{87}{2}\)
