\(419:\left(8\times8\times4,18+0,17\times2,5+2,09\times2\times36+0,23\times2,5\right)\)
\(=419:\left(64\times4,18+0,17\times2,5+4,18\times36+0,23\times2,5\right)\)
\(=419:\left[\left(64+36\right)\times4,18+\left(0,17+0,23\right)\times2,5\right]\)
\(=419:\left[100\times4,18+0,4\times2,5\right]\)
\(=419:\left[418+1\right]\)
\(=419:419\)
\(=1\)
\(=\dfrac{419}{64\cdot4.18+0,17\cdot2,5+2,09\cdot72+0,23\cdot2,5}\)
\(=\dfrac{419}{0,4\cdot2,5+64\cdot4,18+2,09\cdot72}\)
\(=\dfrac{419}{1+418}=1\)