What does integral and rational mean in the following text? The following text is from a textbook about college algebra:
A term is integral and rational in certain literals (letters which represent numbers) if the term consists of (a) positive integer powers of the variables multiplied by a factor not containing any variable, or (b) no variables at all.
For example, the terms $ 6x^2y^3, 5y^4, 7, 4x, {\sqrt 3x^3y^6} $ are integral and rational in the variables present.
However, $3{\sqrt x}$ is not rational in x, ${\frac{4}{x}}$ is not integral in x.
 A: Consider the term $cx^ay^bz^c$, where $x, y, z$ are the variables, and $c$ is a constant coefficient.
We say that this term is integral if $a, b, c$ are non-negative.
We say that this term is rational if $a, b, c$ are integers.
That's my interpretation. It fits the examples given.
A: It means what it literally says.
If the variables (we don't care at all about the constants) are to a positive whole number powers (possibly $1$), or not any variable at all, then we say the term is "integral" and "rational".  If the variables are either to positive whole number powers, not any variable at all, or in the denominator as a power to a whole positive number, it is called "rational".  All "integral" expressions are "rational" but not all rational expressions are integral.  If the expression contains a variable in a denominator (and it's not being canceled out but an equally large or larger power in the numerator) it is "rational" but not "integral".
Anything else (say the varable is under a square root sing or is itself an exponent) is not rational.
This is an abstraction.  The origin referes to  $5, 10, 7\times 3, 8^2 \times 3$ are all integers (and rational) while $\frac 15, \frac {2\times 7}{9}, \frac {51^3}{19^7}$ are rational and $\sqrt {43}, etc.$ are neither.  However in this case we are talking about unknown variables and we don't really care what they actually are; we are concerned with how they are manipulated and represented.
.....
And we don't care AT ALL about the constant factors.... AT ALL.
