c) \(\dfrac{10^2}{9\cdot11}\cdot\dfrac{11^2}{10\cdot12}\cdot\dfrac{12^2}{11\cdot13}\cdot\dfrac{13^2}{12\cdot14}\)
\(=\dfrac{10^2\cdot11^2\cdot12^2\cdot13^2}{9\cdot11\cdot10\cdot12\cdot11\cdot13\cdot12\cdot14}\)
\(=\dfrac{\left(10\cdot11\cdot12\cdot13\right)^2}{\left(9\cdot10\cdot11\cdot12\right)\cdot\left(11\cdot12\cdot13\cdot14\right)}\)
\(=\dfrac{13\cdot10}{9\cdot14}=\dfrac{65}{63}\)
d) \(\left\{\left[\left(\dfrac{7}{8}+\dfrac{1}{2^3}\right)-\left(10-6\right)^2\right]-1^{2024}\right\}:\left(\dfrac{2023}{2024}\right)^0\)
\(=\left\{\left[\left(\dfrac{7}{8}+\dfrac{1}{8}\right)-4^2\right]-1\right\}:1\)
\(=\left(1-16\right)-1\)
\(=1-16-1=-16\)
a) \(\dfrac{-1}{3}+\dfrac{7}{15}+\dfrac{3}{5}\) b) ( -10,56) . 20,35 - 10,56 . 79,65
= \(\dfrac{-5}{15}+\dfrac{7}{15}+\dfrac{9}{15}\) = 10,56 . ( -20,35) - 10,56 . 79,65
= \(\dfrac{\left(-5\right)+7+9}{15}\) = 10,56 . ( (-20,35) - 79,65)
= \(\dfrac{-11}{15}\) = 10,56 . (-100)
= -1056
