Algebra-1

Question Analysis
This question tests the student's ability to apply the Product of Powers Rule to identify equivalent expressions.

Key Concept Explanation
The Product of Powers Rule states that when multiplying two or more powers with the same base, you add their exponents. For any non-zero number $$ a $$ and integers $$ m $$, $$ n $$, $$ a^m \cdot a^n = a^{m+n} $$.

Step-by-step Solution
1. Identify the key concept:  The Product of Powers Rule.
2. Apply the rule to each option:
Option A: $$w^5 \cdot w^3 = w^{5+3} = w^{8}$$
Option B: $$w^4 \cdot w^2 = w^{4+2} = w^{6}\neq w^{8}$$
Option C: $$w^{11} \cdot w^{-3} = w^{11+(-3)} = w^{8}$$
Option D: $$w^8 \cdot w = w^{8+1} = w^{9}\neq w^{8}$$.
Option E: $$w^4 + w^2$$ ...