Question 267388
I think I have all 6 ways:

(1) 
{{{125^(-4/3)}}
{{{5^-4}}
{{{1/5^4}}}
{{{1/625}}}
---
(2) 
{{{125^(-4/3)}}
{{{(1/125)^(4/3)}}}
{{{(1/5)^4}}}
{{{1/625}}}
---
(3)
{{{125^(-4/3)}}
{{{(5^3)^(-4/3)}}}
{{{5^(-4)}}}
{{{(1/5)^4}}}
{{{1/625}}}
---
(4)
{{{125^(-4/3)}}
{{{(5^3)^(-4/3)}}}
{{{(1/(5^3))^(4/3)}}}
{{{(1/5)^(4)}}}
{{{1/625}}}
---
(5)
{{{125^(-4/3)}}
{{{(5^3)^(-4/3)}}}
{{{(5^(-12))^(1/3)}}}
{{{5^(-4)}}}
{{{1/625}}}
---
(6) 
{{{125^(-4/3)}}
{{{(125^(-4))^(1/3)}}}
{{{((5^3)^(-4))^(1/3)}}}
{{{(5^(-12))^(1/3)}}}
{{{5^(-4)}}}
{{{1/625}}}