how do I simplify (y^3)^3 without parentheses?
We multiply the exponents outside of the parenthesis to all the exponents inside the parenthesis.
\(\sf(y^3)^3\rightarrow~y^{3\times3}\rightarrow~\boxed{\sf~y^9}\)
We will use this property in exponents to answer your question:
\(\sf{(a^b)^c=a^{b\times c}}\)
So basically we multiply the exponents when it is outside of the parenthesis. So:
\(\sf{(y^3)^3=y^{3\times3}}\)
\(\sf{=y^9}\)
So your answer would be \(\boxed{\sf{y^9}}\)