Question 27137
There are 3 ways you can go about solving this Question. 

The easiest way is already mentioned in your question itself and you havent even realised it!!

We have {{{(5/4)^(-2)}}} and {{{(5/4)^2}}} 
Since both have the same number i.e.{{{5/4}}} all you had to do was add their exponents
But we know that -2 +2 = 0
So basically we are left with 1
{{{((4/5)^3)*1}}} = {{{64/25}}}


You've tried the 2nd way so let me finish that one too
Since you are writin everything in terms of 4/5,let's write the last term also(the one with the positive power)in terms of 4/5 as well
{{{(4/5)^(-2)}}}

{{{((4/5)^3)((4/5)^2)(4/5)^(-2)}}}

Adding the exponents only now we get  3-2+2 = 3
or {{{(4/5)^3}}} = {{{64/25}}} 

Same as above. Yay!!