We will use this property in exponents to answer your question:
[tex]\sf{(a^b)^c=a^{b\times c}}[/tex]
So basically we multiply the exponents when it is outside of the parenthesis. So:
[tex]\sf{(y^3)^3=y^{3\times3}}[/tex]
[tex]\sf{=y^9}[/tex]
So your answer would be [tex]\boxed{\sf{y^9}}[/tex]