What is the simplified form of the expression k^3(k7/5)^-5

k^3(k7/5)^-5 can be rewritten as (k^3) * (7k/5)^(-5) (must use parentheses around that "-5").

This would be better written as 

k^3                   k^3 * 5^5
------------ = -------------------  
(7k/5)^5       7^5 * k^5 

Then k^3 / k^5 reduces to 1 / k^2, and 5^5 / 7^5 reduces to 1 / 5^2, or 1 / 25.
 
Thus, 

the answer in simplest form is

                                      1                                               
                                -----------
                                  25k^2