(3ав²) ³

To simplify the expression \((3av^2)^3\), you apply the power of a product property, which states that \((ab)^n = a^n \cdot b^n\).

So, we can break it down as follows:

\[ (3av^2)^3 = 3^3 \cdot (a)^3 \cdot (v^2)^3 \]

Now calculate each part:

\[ 3^3 = 27, \] \[ (a)^3 = a^3, \] \[ (v^2)^3 = v^{2 \cdot 3} = v^6. \]

Putting it all together:

\[ (3av^2)^3 = 27a^3v^6. \]

Thus, the simplified expression is:

\[ \boxed{27a^3v^6}. \]