b. \( \left(2 x^{4}\right)^{3} \)

To simplify \( \left(2 x^{4}\right)^{3} \), use the power of a product property, which states that \( (ab)^n = a^n b^n \). This means you can distribute the exponent to both the number and the variable. In this case, you would get \( 2^3 \) and \( (x^4)^3 \), leading to \( 8x^{12} \). So, \( \left(2 x^{4}\right)^{3} = 8x^{12} \)! Now, wanting to see the beauty of exponents? Remember, when you multiply powers with the same base, you add the exponents. That’s what you’ll do with \( x^4 \) raised to the third power, resulting in \( x^{4 \times 3} = x^{12} \). Mathematics is all about patterns; once you spot them, the rest becomes a delightful puzzle!