Final answer:
The operation (2/3) × (2/3) × (2/3) is the cubing of the fraction 2/3, resulting in (2^3)/(3^3) or 8/27. It exemplifies the multiplication of fractions and the principle of exponentiation.
Step-by-step explanation:
The student is performing a mathematical operation involving the cubing of a fraction. Specifically, the question asks to calculate the cube of the fraction (2/3), which means to multiply the fraction by itself three times: (2/3) × (2/3) × (2/3). To do this, we apply the rules for multiplication of fractions: multiply the numerators together and multiply the denominators together. Thus, the calculation becomes (2 × 2 × 2)/(3 × 3 × 3) = 8/27. This outcome demonstrates the process of exponentiation of fractions, where (a/b)^n = a^n / b^n.