Notation for an Unknown in an Equation that Represents a New Variable with Every Invocation?

Question

If you have:

a*a*a

you can represent it as:

a^3

Is there a similar notation to collapse

a*b*c

to some form:

?^3

where ? represents "a", "b", and "c" (different quantities) multiplied together?

Answer 1

One thing we could do is index our variables using subscripts: $$ (x_1)(x_2)\cdots(x_{999})(x_{1000}) = \prod_{n=1}^{1000} x_n $$

Answer 2

No. You have $2\cdot 3\cdot 4=24$ what is not a cube (in integers or rationals). You can say it is a cube if we are allowed to work in real numbers. So, let us have a look at other example. Consider the polynomial $x\cdot (x+1) \cdot (x+2)=x^3+3x^2+2x.$ It is not the cube of any polynomial.