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Answer 1 · 2017-08-24T17:57:32

#=root24(a^7b^13)#

Let's write the roots as indices.

#(root8(a^5b^7))/(root3(ab)) = (a^(5/8)b^(7/8))/(a^(1/3)b^(1/3)#

When dividing, subtract the indices of like bases.

#a^(5/8-1/3) xx b^(7/8-1/3)#

#= a^((15-8)/24) xx b^((21-8)/24)#

#= a^(7/24) xxb^(13/24)#

#=root24(a^7b^13)#