(3x²y⁴)⁴ / 9x²(y³)⁴
Simplify the numerators first.
3x⁶y⁸ / 9x²y7
Now, divide the two together, and cross out the exponents as you simplify them.
Now, divide 3 from 9, and get 3. Then, divide x⁶ from x² and get x⁴. Finally, you divide y⁸ from y⁷ and get y.
Put those all together :
1x⁴y / 3
Simplify.

~Hope I helped!~