Respuesta :

Answer:

  x^(-1/12)y^(-19/8)

Step-by-step explanation:

There are three rules of exponents that apply here:

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(b·c)

  1/a^b = a^-b

Using these rules the expression simplifies as ...

[tex]\displaystyle\frac{x^{\frac{1}{2}}y^{-\frac{5}{4}}\left(x^{\frac{1}{6}}y^{-\frac{1}{4}}\right)^{\frac{1}{2}}}{x^{\frac{2}{3}}y^{1}}=x^{\frac{1}{2}+\frac{1}{6}\cdot\frac{1}{2}-\frac{2}{3}}y^{-\frac{5}{4}-\frac{1}{4}\cdot\frac{1}{2}-1}=x^{-\frac{1}{12}}y^{-\frac{19}{8}}[/tex]

So, the simplified expression is ...

  x^(-1/12)y^(-19/8)