Final answer:
The expression (4g3h2k4)3 is equivalent to 64g9h6k12.
Step-by-step explanation:
The expression (4g3h2k4)3 can be simplified by applying the rule of multiplying exponentiated quantities. To do this, we cube the number term 4 and multiply the exponent of each variable term by 3. Since the variables g, h, and k have no numerical coefficients, their exponents are already 1. Therefore, the equivalent expression is:
(4g3h2k4)3 = 43g3 × 31h2 × 34k4 = 64g9h6k12