Option D:
is the expression equivalent to 
Explanation:
Option A: 
The expression can be written as 
Applying exponent rule, we get,

Thus, the expression
is not equivalent to the expression 
Hence, Option A is not the correct answer.
Option B: ![\sqrt[9]{xy^2}](https://tex.z-dn.net/?f=%5Csqrt%5B9%5D%7Bxy%5E2%7D)
The expression can be written as 
Applying exponent rule, we get,

Thus, the expression
is not equivalent to the expression 
Hence, Option B is not the correct answer.
Option C: 
The expression can be written as 
Applying exponent rule, we get,

Thus, the expression
is not equivalent to the expression 
Hence, Option C is not the correct answer.
Option D: ![x\sqrt[9]{y^{2} }](https://tex.z-dn.net/?f=x%5Csqrt%5B9%5D%7By%5E%7B2%7D%20%7D)
The expression can be written as 
Applying exponent rule, we get,

Thus, the expression
is equivalent to the expression 
Hence, Option D is the correct answer.