What do these symbols in pre-algebra mean?

That is another way to raise a number to a power.

Ex: 5^2=25

The "*" symbol is another way to specify multiplication. You've probably only seen the symbol that looks like an "x". Once you get into algebra, you will see that letters are combined with numbers to make expressions. The letter "x" is the most commonly used letter in algebra. Because the multiplication symbol looks so much like an "x" (and is often typed with the "x" key, like I'm doing here), the "*" symbol was devised as an alternative to avoid confusion.

(^) this symbol represent power ex- [2^3= 8]

2 to the power 3 is equal to 8

(*) This symbol represent multiplication ex- [2*3=6]

2 multiplied by 3 is equal to 6