Final answer:
The principal root of 3√(-216/729) is simplified to -2/3 which is equivalent to -6/9, matching the option (A) -6/9.
Step-by-step explanation:
To find the principal root of the cube root section of the expression 3√(-216/729), we first simplify the fraction inside the cube root.
-216 divided by 729 simplifies to -8/27 because both numbers are divisible by 27.
Taking the cube root of -8/27 gives us -2/3 because the cube root of -8 is -2 and the cube root of 27 is 3.
Therefore, the correct answer is -2/3, which is equivalent to -6/9 after multiplying the numerator and denominator by 3 to match the options provided. The correct answer is represented by option (A) -6/9.