a: \(\left(\dfrac{3}{7}\right)^0\cdot1^{15}+\dfrac{7}{9}:\left(\dfrac{2}{3}\right)^2-\dfrac{4}{5}\)
\(=1\cdot1+\dfrac{7}{9}:\dfrac{4}{9}-\dfrac{4}{5}\)
\(=\dfrac{1}{5}+\dfrac{7}{4}=\dfrac{4}{20}+\dfrac{35}{20}=\dfrac{39}{20}\)
b: \(\left(\dfrac{3}{2}\right)^2-\left[0,5:2-9\cdot\left(-\dfrac{1}{2}\right)^2\right]\)
\(=\dfrac{9}{4}-\left[\dfrac{1}{2}:2-9\cdot\dfrac{1}{4}\right]\)
\(=\dfrac{9}{4}-\dfrac{1}{4}+\dfrac{9}{4}=\dfrac{17}{4}\)
c: \(\left\{\left[\left(\dfrac{1}{25}-0,6\right)^2:\dfrac{49}{125}\right]\cdot\dfrac{5}{6}\right\}-\left[\left(-\dfrac{1}{3}\right)+\dfrac{1}{2}\right]\)
\(=\left\{\left[\left(\dfrac{1}{25}-\dfrac{15}{25}\right)^2\cdot\dfrac{125}{49}\cdot\dfrac{5}{6}\right]\right\}-\dfrac{1}{6}\)
\(=\left[\left(-\dfrac{14}{25}\right)^2\cdot\dfrac{125}{49}\cdot\dfrac{5}{6}\right]-\dfrac{1}{6}\)
\(=\dfrac{196}{625}\cdot\dfrac{125}{49}\cdot\dfrac{5}{6}-\dfrac{1}{6}\)
\(=\dfrac{196}{49\cdot6}-\dfrac{1}{6}=\dfrac{4}{6}-\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}\)
d: \(2\left[\left(7-3^3:3^2\right):2^2+99\right]-100\)
\(=2\cdot\left[\left(7-3\right):4+99\right]-100\)
\(=2\left(1+99\right)-100=100\)
\(a,\left(\dfrac{3}{7}\right)^0.1^{15}+\dfrac{7}{9}:\left(\dfrac{2}{3}\right)^2-\dfrac{4}{5}\)
\(=1.1+\dfrac{7}{9}:\dfrac{4}{9}-\dfrac{4}{5}\)
\(=1+\dfrac{7}{4}-\dfrac{4}{5}\)
\(=\dfrac{20}{20}+\dfrac{35}{20}-\dfrac{16}{20}\)
\(=\dfrac{39}{20}\)
\(b,\left(\dfrac{3}{2}\right)^2-\left[0,5:2-9.\left(\dfrac{-1}{2}\right)^2\right]\)
\(=\dfrac{9}{4}-\left[\dfrac{1}{2}.\dfrac{1}{2}-9.\dfrac{1}{4}\right]\)
\(=\dfrac{9}{4}-\left[\dfrac{1}{4}-\dfrac{9}{4}\right]\)
\(=\dfrac{9}{4}-\dfrac{-8}{4}\)
\(=\dfrac{17}{4}\)
\(c,\left\{\left[\left(\dfrac{1}{25}-0,6\right)^2:\dfrac{49}{125}\right].\dfrac{5}{6}\right\}-\left[\left(\dfrac{-1}{3}\right)+\dfrac{1}{2}\right]\)
\(=\left\{\left[\left(\dfrac{1}{25}-\dfrac{3}{5}\right)^2.\dfrac{125}{49}\right].\dfrac{5}{6}\right\}-\left[\dfrac{-2}{6}+\dfrac{3}{6}\right]\)
\(=\left\{\left[\left(\dfrac{1}{25}-\dfrac{15}{25}\right)^2.\dfrac{125}{49}\right].\dfrac{5}{6}\right\}-\dfrac{1}{6}\)
\(=\left\{\left[\left(\dfrac{-14}{25}\right)^2.\dfrac{125}{49}\right].\dfrac{5}{6}\right\}-\dfrac{1}{6}\)
\(=\left\{\left[\dfrac{196}{625}.\dfrac{125}{49}\right].\dfrac{5}{6}\right\}-\dfrac{1}{6}\)
\(=\left\{\left[\dfrac{4.1}{5.1}\right].\dfrac{5}{6}\right\}-\dfrac{1}{6}\)
\(=\left\{\dfrac{4}{5}.\dfrac{5}{6}\right\}-\dfrac{1}{6}\)
\(=\dfrac{4}{6}-\dfrac{1}{6}\)
\(=\dfrac{3}{6}=\dfrac{1}{2}\)
\(d,2.\left[\left(7-3^3:3^2\right):2^2+99\right]-100\)
\(=2.\left[\left(7-3^{3-2}\right):4+99\right]-100\)
\(=2.\left[\left(7-3\right):4+99\right]-100\)
\(=2.\left[4:4+99\right]-100\)
\(=2.\left[1+99\right]-100\)
\(=2.100-100\)
\(=200-100\)
\(=100\)
