Simplify (⅔)² × (⁸/⁹) × 27: Step-by-Step Solution

To solve this problem, we need to follow the order of operations (PEMDAS/BODMAS), which states that we should perform any calculations inside parentheses first, then exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Let's break down the problem step by step:

(⅔)² = 4/9

Now, let's multiply the result by (⁸/⁹):

(4/9) × (⁸/⁹) = (4 × 8) / (9 × 9) = 32/81

Finally, let's multiply the result by 27:

(32/81) × 27 = (32 × 27) / 81 = 864/81

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:

864/81 = (96 × 9) / (9 × 9) = 96/9 = 32/3

Therefore, (⅔)² × (⁸/⁹) × 27 is equal to 32/3.