1. Problem: Simplify the expression $$\frac{2x^{4/3} \cdot x^{2/3}}{x^2}$$. 2. Formula and rules: When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$. When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. Apply multiplication rule to numerator: $$2x^{4/3} \cdot x^{2/3} = 2x^{4/3 + 2/3} = 2x^{6/3} = 2x^2$$ 4. Now the expression is: $$\frac{2x^2}{x^2}$$ 5. Apply division rule: $$\frac{2\cancel{x^2}}{\cancel{x^2}} = 2$$ 6. Final answer: $$2$$