1. The problem is to simplify the expression $$\frac{3}{4} \times \frac{3}{3} \cdot \frac{2}{1}^0 \times \frac{1}{3} \times \frac{1}{3} \times \frac{2}{1}$$. 2. Recall the rules: - Any number raised to the power 0 is 1, so $$\left(\frac{2}{1}\right)^0 = 1$$. - Multiplying fractions: multiply numerators together and denominators together. 3. Substitute and simplify step-by-step: $$\frac{3}{4} \times \frac{3}{3} \times 1 \times \frac{1}{3} \times \frac{1}{3} \times \frac{2}{1}$$ 4. Simplify $$\frac{3}{3} = 1$$, so the expression becomes: $$\frac{3}{4} \times 1 \times 1 \times \frac{1}{3} \times \frac{1}{3} \times \frac{2}{1} = \frac{3}{4} \times \frac{1}{3} \times \frac{1}{3} \times \frac{2}{1}$$ 5. Multiply numerators: $$3 \times 1 \times 1 \times 2 = 6$$ 6. Multiply denominators: $$4 \times 3 \times 3 \times 1 = 36$$ 7. So the product is: $$\frac{6}{36}$$ 8. Simplify the fraction by dividing numerator and denominator by 6: $$\frac{6 \div 6}{36 \div 6} = \frac{1}{6}$$ Final answer: $$\frac{1}{6}$$.