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