\(\left(2^3\cdot9^4+9^3\cdot45\right):\left(9^2\cdot10-9^2\right)\)
\(=\left(2^3\cdot3^8+3^6\cdot5\cdot3^2\right):\left[9^2\cdot\left(10-1\right)\right]\)
\(=\left(2^3\cdot3^8+3^8\cdot5\right):\left(9^2\cdot9\right)\)
\(=\left[3^8\cdot\left(2^3+5\right)\right]:9^3\)
\(=3^8\cdot13:3^6\)
\(=3^2\cdot13\)
\(=117\)
\(\left(2^3.9^4+9^3.45\right):\left(9^2.10-9^2\right)\)
\(=\left(2^3.3^8+3^6.3^2.5\right):\left(3^4.10-3^4\right)\)
\(=\left(2^3.3^8+3^8.5\right):\left(3^4.\left(10-1\right)\right)\)
\(=3^8\left(2^3+5\right):3^4.9=3^8\left(2^3+5\right):3^6\)
\(=3^2.13=9.13=117\)
