How do you simplify # ""^5sqrt(96)#

2 Answers
Oct 25, 2014

#root 5 96#

#=> root 5 (2^5*3)#

#=> root 5 (2^5) * root 5 3#

#=> 2root 5 3#

Oct 25, 2014

Since #96=2^5cdot3#,

#root[5]{96}=root[5]{2^5cdot3}#

by distributing the 5th-root,

#=root[5]{2^5}cdot root[5]{3}#

by cancelling out the 5th-power and the 5th-root,

#=2 root[5]{3}#.


I hope that this was helpful.