How do you simplify #root3(16)*root3(4)#?

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Answer 1 · 2016-08-22T09:49:56

#root3(16)*root3(4)=4#

#root3(16)*root3(4) = root3(2^4)*root3(2^2)#

#= root3(2^(4+2)) = root3(2^6)#

#=2^(6/3) = 2^2 = 4#

Answer 2 · 2016-08-22T09:58:56

4

Method 1)
#root3(16)*root3(4)#= #root3(16*4)#=#root3(64)#=4

Method2)
#root3(16)# =#16^(1/3)#
16 = #4^2#

#16^(1/3)#= #(4^2)^#
=#4^(2/3)#

But #root3(4)#=#4^(1/3)#
So
#root3(16)*root3(4)# =#4^(2/3)*4^(1/3)#=4