Final answer:
The simplest form of the radical expression 4 ⁴√2x + 6⁴√2x is achieved by adding the coefficients, resulting in 10⁴√2x.
Step-by-step explanation:
To find the simplest form of the radical expression 4 ⁴√2x + 6⁴√2x, we can combine like terms. Since the radical expressions have the same index and radicand, we can add them just like algebraic terms. Think of it like adding variables, where if you have a apples and you add b more apples, you end up with a+b apples. Therefore, we can directly add the coefficients (4 and 6) of the radical terms because the radical parts are identical.
The expression simplifies as follows:
4⁴√2x + 6⁴√2x = (4 + 6)⁴√2x = 10⁴√2x.
Thus, the simplest form of the radical expression is 10⁴√2x.