How did this third force come from? We need to define that the cube root of x is a power of x, such as a power, and write it in the form of x a, which is a new definition. You can equate one with several things you have never seen before. In any case, this is a new definition. But we always hope that the definition is simple or does not conflict with what we already have. Then we think of the definition of (1) root. What does it mean that X is cubic? That is, the cube of a certain number is x, and this number is the cube of x, so there must be (x a)? =x .(2) There is a formula in the power operation, (x m) n = x (Mn) (that is, the m power of x and then the n power is equal to the Mn power of x). This formula was originally only applicable to positive integers m and n. Now think about it, in order to define this result more simply, must X A still satisfy this formula (although A is not an integer)? So (x a)? = x (3a) = x so 3a= 1, a= 1/3. In this way, we define that the third power of X is the third power of X, which is consistent with the original formula (X M) n = X (Mn), but if you define A as another number, it will not be consistent with this formula.
It can also be seen from the above process that when defining a new thing in mathematics, it is often necessary to make it not conflict with the original conclusion, and such a definition is a good definition. Even if the definition of a difficult problem is bound to conflict with the original problem, we should try our best to reduce the conflict. The landlord can also understand and remember the knowledge points of mathematical memory in this way. Many things in mathematics are related to existing conclusions, so there is no need to recite them as new things. Even in English words, there are many things that are the same as the original root or with an affix, so we should also pay attention to memory skills.