To find the sum of the exponents of the variables in the expression [tex]\(6 w x y^3 z^2\)[/tex], we follow these steps:
1. Identify and note the exponent of each variable:
- The exponent of [tex]\(w\)[/tex] is [tex]\(1\)[/tex]. If no exponent is explicitly written, it is understood to be [tex]\(1\)[/tex].
- The exponent of [tex]\(x\)[/tex] is [tex]\(1\)[/tex] for the same reason.
- The exponent of [tex]\(y\)[/tex] is explicitly [tex]\(3\)[/tex].
- The exponent of [tex]\(z\)[/tex] is explicitly [tex]\(2\)[/tex].
2. Add up all the exponents of the variables:
[tex]\[
1 + 1 + 3 + 2 = 7
\][/tex]
Therefore, the sum of the exponents of the variables in the expression [tex]\(6 w x y^3 z^2\)[/tex] is [tex]\(\boxed{7}\)[/tex].
