已知2^m=a,化简16×2^2m-1 ×2^3m-1 -4^m ×8^m

题目

已知2^m=a,化简16×2^2m-1 ×2^3m-1 -4^m ×8^m

答案

16×2^2m-1 ×2^3m-1 -4^m ×8^m
=2^4*2^(2m-1)*2(3m-1)-2^(2m)*2^(3m)
=2^(4+2m-1+3m-1)-2^(5m)
=2^(2+5m)-2^(5m)
=4*2^(5m)-2^(5m)
=3*2^(5m)
=3*(2^m)^5
=3a^5