There is a pattern here. After each job, the amount of pennies received is multiplied by 4.
1st: 4 pennies = 4^1
2nd: 16 pennies = 4^2
3rd: 64 pennies = 4^3
4th: 64*4 = 4^4 = 256 pennies
To find the payment for the 9th grooming job, you multiply by 4 nine times which is the same as raising 4 to the 9th power: 4^9. Solve that to get your answer of 262144 pennies.
The equation is y = 4^x where x is the number of grooming job