\(81^{10}-27^{13}-9^{21}\)
\(=\left(3^4\right)^{10}-\left(3^3\right)^{13}-\left(3^2\right)^{21}\)
\(=3^{40}-3^{39}-3^{42}\)
\(=3^{39}\left(3-1-3^3\right)\)
\(=3^{39}.\left(-25\right)\)
\(=3^{37}.3^2.\left(-25\right)\)
\(=3^{37}.\left(-225\right)⋮225\)
\(\Leftrightarrow81^{10}-27^{13}-9^{21}⋮225\left(đpcm\right)\)