[tex]\displaystyle\bf\\a)~~2^{10}\cdot32=2^{10}\cdot2^5=2^{10+5}=\boxed{\bf2^{15}}\\\\b)~~81\cdot3^7\cdot3^8=3^4\cdot3^7\cdot3^8=3^{4+7+8}=\boxed{\bf3^{19}}\\\\c)~~2^{17}\cdot4^5=2^{17}\cdot\Big(2^2\Big)^5=2^{17}\cdot2^{2\times5}=2^{17}\cdot2^{10}=2^{17+10}=\boxed{\bf2^{27}}[/tex]
