[tex] \frac{ ({x}^{1} {y}^{ \frac{1}{4} })^{2} }{ {x}^{ \frac{5}{4} } {y}^{ \frac{5}{8} } } \\ \frac{ {x}^{2} {y}^{ \frac{2}{4} } }{ {x}^{ \frac{5}{4} } {y}^{ \frac{5}{8} } } \\ \frac{ {x}^{2} {y}^{ \frac{1}{2} } }{ {x}^{ \frac{5}{4} } {y}^{ \frac{5}{8} } } \\ [/tex]
You can distribute the exponent outside of the parentheses by multiplying it to the exponent in each term in the numerator
When dividing, subtract the exponent of the numerator by the exponent of the denominator for each variable
For x:
[tex] {x}^{2} - {x}^{ \frac{5}{4} } \\ {x}^{ \frac{3}{4} } [/tex]
For y:
[tex] {y}^{ \frac{1}{2} } - {y}^{ \frac{5}{8} } \\ {y}^{ \frac{ - 1}{8} } \\ \sqrt[8]{y} [/tex]
EDIT: y^(-1/8) is equal to 1 / (8 radical y)
Final answer:
[tex] \frac{ {x}^{ \frac{3}{4} } }{ \sqrt[8]{y} } [/tex]
