Let me give some complements.
First, these terms are quite general. For example, 和 is also used in direct sum, 积 is also used for tensor product, Cartesian product and product space. 商 is also used for quotient space, quotient topology and so on.
Similarly, the result of $a^b$ is called 幂mi4 where "a" is called 底数 and "b" is called 指数.
These are really traditional terminology in chinese before the modern time, therefore more or less related to some ancient chinese convention or grammar. For example, in division, 3/2 can be stated as 二除三 or equivalently 三除以二, pay attention to the word "以" which means "by".
Perhaps you will be interested in some other traditional chinese words in mathmatics. In ancient chinese, the mathematics is called “算术”, namely the "technique of computation", but now we call it "数学", namely the "study of number".
And one of my favourite Chinese theorems goes like “缘幂势既同，则积不容异”, concise and precise.
For elementary mathematics terminology, it is sufficient to look up something like "mathematics dictionary for primary students", which I think more efficient for you.
Personally, I strongly recommend you read the book by Li Wenwei who has both deep knowledge to algebra and elegant style of chinese math writing. See 李文威的学术主页