Answer:
[tex]8b\sqrt{2ab}[/tex]
Step-by-step explanation:
Rewrite 128a[tex]b^{3}[/tex] as [tex](8b)^{2}[/tex] ⋅ (2ab).
Factor 64 out of 128.
[tex]\sqrt{64 (2)ab^{3} }[/tex]
Rewrite 64 as [tex]8^{2}[/tex] .
[tex]\sqrt{8^{2} . 2ab^{3}[/tex]
Factor out [tex]b^{2}[/tex].
[tex]\sqrt{8^{2} . 2a (b^{2}b)[/tex]
Move a.
[tex]\sqrt{8^{2} . 2b^{2}ab[/tex]
Move 2.
[tex]\sqrt{8^2b^2 . 2ab}[/tex]
Rewrite [tex]8^{2} b^{2}[/tex] as [tex](8b)^{2}[/tex].
[tex]\sqrt{(8b)^2 . 2 (ab)}[/tex]
Add parentheses.
[tex]\sqrt{(8b)^2 . (2ab)}[/tex]
Pull terms out from under the radical.
[tex]8b\sqrt{2ab}[/tex]
