Answer:
Option 1 - x to the 14th power over y to the 18th power
Step-by-step explanation:
Given : The quantity of x to the 7th power over y to the 9th power all raised to the 2nd power.
To find : Choose the correct simplification of the quantity?
Solution : 
The quantity of x to the 7th power i.e.,  .....(1)
  .....(1)
Then the quantity y to the 9th power i.e.,   .....(2)
 .....(2)
According to question,
Equation 1 is over equation 2,
i.e.,   
 
And The resultant raised to the 2nd power.
i.e.,  
 
Simplify it by taking power inside, 
  
 
  
 
Which means x to the 14th power over y to the 18th power.
Therefore, Option 1 is correct.