Fractional index.

[sensational]

How to write with fractional index?
(1/5x^2)^-2(x^3y^4)

 

[Harry_the_cat]

Is this what you mean?
\(\displaystyle (\frac{1}{5}x^2)^{-2}(x^3y^4)\)

or this
\(\displaystyle (\frac{1}{5x^2})^{-2}(x^3y^4)\)

 

[sensational]

The first one

 

[Harry_the_cat]

There will be no fractional index involved. But you could write the whole expression as a fraction.
To expand the first bracket you need a combo of some of the index laws. Have you had a go?