Answer:
The simplified form is: [tex]\frac{1}{2}x^{\frac{1}{4}}y^{-\frac{1}{6}}[/tex] or [tex]\frac{x^{\frac{1}{4}}}{2y^{\frac{1}{6}}}[/tex]
Step-by-step explanation:
So we need to find the simplified form of:
[tex]\frac{2x^{\frac{1}{2}}y^{\frac{2}{3}}}{4x^{\frac{1}{4}}y^{\frac{5}{6}}}[/tex]
We know that:
(a^m)/(a^n) = a^(m-n)
Then:
[tex]\frac{2}{4}x^{\frac{1}{2} - \frac{1}{4} }y^{\frac{2}{3}-\frac{5}{6}}[/tex]
Simplifien the expression:
[tex]\frac{1}{2}x^{\frac{1}{4}}y^{-\frac{1}{6}}[/tex]
So, the simplified form is:
[tex]\frac{1}{2}x^{\frac{1}{4}}y^{-\frac{1}{6}}[/tex] or [tex]\frac{x^{\frac{1}{4}}}{2y^{\frac{1}{6}}}[/tex]
