3. \( \left(8 a^{6} b^{12}\right)^{\frac{1}{3}} \)

To simplify \( \left(8 a^{6} b^{12}\right)^{\frac{1}{3}} \), we can apply the exponent to each factor inside the parentheses. This gives us: \[ \left(8\right)^{\frac{1}{3}} \cdot \left(a^{6}\right)^{\frac{1}{3}} \cdot \left(b^{12}\right)^{\frac{1}{3}} \] Calculating each part separately, we find: 1. \( \left(8\right)^{\frac{1}{3}} = 2 \) (since \( 2^3 = 8 \)) 2. \( \left(a^{6}\right)^{\frac{1}{3}} = a^{6 \cdot \frac{1}{3}} = a^{2} \) 3. \( \left(b^{12}\right)^{\frac{1}{3}} = b^{12 \cdot \frac{1}{3}} = b^{4} \) Putting it all together, we have: \[ \left(8 a^{6} b^{12}\right)^{\frac{1}{3}} = 2 a^{2} b^{4} \] So the simplified expression is \( 2 a^{2} b^{4} \).