This can answered in one line, but to demonstrate the how the exponents work we need to write down every step.
(3y)^17 3(y)^9
rewrite so that each term has its own exponent
= 3^17 y^17/(3^1 y^9)
convert the division to multiplication by changing the sign of the denominator's exponents (quotient property)
= 3^17 y^17 3^-1 y^-9
combine exponents of like terms
= 3^(17-1) y^(17-9)
perform the additions within the exponents
= 3^16 y^8
Once you understand the process, you should simply be able to get the answer on inspection.
Once you have that familiarity with the process, you will think through the problem in this manner: You have seventeen 3s in the numerator and one in the denominator, that means you have sixteen 3s. You have seventeen ys in the numerator and 9 ys in the denominator, that leaves you with eight ys.
