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)
