\(a)4\cdot8\cdot16^2=2^2\cdot2^3\cdot\left(2^4\right)^2=2^5\cdot2^8=2^{13}\\ b)4^3\cdot64=\left(2^2\right)^3\cdot2^6=2^6\cdot2^6=2^{12}\\ c)3^4\cdot9\cdot27^2=3^4\cdot3^2\cdot\left(3^3\right)^2=3^4\cdot3^2\cdot3^6=3^{12}\\ d)16^2\cdot9^4=\left(2^4\right)^2\cdot\left(3^2\right)^4=2^8\cdot3^8=\left(2\cdot3\right) ^8=6^8\\ e)25\cdot5\cdot125=5^2\cdot5\cdot5^3=5^6\\ g)81\cdot3^3=3^4\cdot3^3=3^7\\ h)125^2\cdot25^4=\left(5^2\right)^2\cdot\left(5^2\right)^4=5^4\cdot5^8=5^{12}\\ i)4^2\cdot25=4^2\cdot5^2=\left(4\cdot5\right)^2=20^2\)
a)4⋅8⋅162=22⋅23⋅(24)2=25⋅28=213b)43⋅64=(22)3⋅26=26⋅26=212c)34⋅9⋅272=34⋅32⋅(33)2=34⋅32⋅36=312d)162⋅94=(24)2⋅(32)4=28⋅38=(2⋅3)8=68e)25⋅5⋅125=52⋅5⋅53=56g)81⋅33=34⋅33=37h)1252⋅254=(52)2⋅(52)4=54⋅58=512i)42⋅25=42⋅52=(4⋅5)2=202