3. Simplify: a) \( \left(2 a^{2} b^{3} c\right)^{3} \)

To simplify \( \left(2 a^{2} b^{3} c\right)^{3} \), you will want to use the power of a product rule which states that \( (xy)^n = x^n y^n \). So, applying this, we distribute the exponent 3 across each component: \[ \left(2 a^{2} b^{3} c\right)^{3} = 2^{3} \cdot \left(a^{2}\right)^{3} \cdot \left(b^{3}\right)^{3} \cdot \left(c\right)^{3} = 8 a^{6} b^{9} c^{3} \] Thus, the simplified result is \( 8a^{6} b^{9} c^{3} \).