[xy^5 / x^-4 y^2]^-2?

Question

Please explain it on a easy way. Thank you

Answer 1

negative exponents flip the variable from denominator to numberator, or vice versa:

[x^5y^5 / y^2]^-2
[x^5y^3]^-2
[1 / x^5y^3]^2
1/ x^10y^6

Answer 2

[xy^5 / x^-4 y^2]^-2

[xy^5 / (y^2/x^4)]^-2 [invert x^-4 into 1/x^4 and multiply with y^2]

[x^5y^5/y^2]^-2 [invert (y^2/x^4) and multiply with xy^5]

[x^5y^3]^-2 [divide y^5 by y^2 making it y^3]

[1/(x^5y^3)]^2 [invert the whole thing to remove the negative exponent]

1/(x^10y^6) [square the term] [(x^5)^2=x^(5*2)]

-//-//-

Answer 3

Consider contents of bracket first of all.
(x) (x)^4 y^(5) y^(- 2)
x^5 y ³

Now have:-
[ x^5 y ³ ]^(- 2)
= 1 / [ x^5 y ³ ] ²
= 1 / [ (x^10)(y^6) ]