To find the sum of the exponents of the variables in the expression [tex]\(6 w x y^3 z^2\)[/tex], let's break it down step-by-step:
1. Identify the variables and their exponents:
- The variable [tex]\(w\)[/tex] has an exponent of 1 (since [tex]\(w\)[/tex] can be written as [tex]\(w^1\)[/tex]).
- The variable [tex]\(x\)[/tex] has an exponent of 1 (since [tex]\(x\)[/tex] can be written as [tex]\(x^1\)[/tex]).
- The variable [tex]\(y\)[/tex] has an exponent of 3 (as shown in the expression [tex]\(y^3\)[/tex]).
- The variable [tex]\(z\)[/tex] has an exponent of 2 (as shown in the expression [tex]\(z^2\)[/tex]).
2. List out the exponents:
- [tex]\(w\)[/tex] has an exponent of 1.
- [tex]\(x\)[/tex] has an exponent of 1.
- [tex]\(y\)[/tex] has an exponent of 3.
- [tex]\(z\)[/tex] has an exponent of 2.
3. Sum the exponents:
- Add the exponents together: [tex]\(1 + 1 + 3 + 2\)[/tex].
4. Calculate the total:
- [tex]\(1 + 1 = 2\)[/tex]
- [tex]\(2 + 3 = 5\)[/tex]
- [tex]\(5 + 2 = 7\)[/tex]
Therefore, the sum of the exponents of the variables in the expression [tex]\(6 w x y^3 z^2\)[/tex] is [tex]\(7\)[/tex].
