Final answer:
The expression 512^-4/3 with positive exponents is written as A. 1/512^4/3, by applying the rule of negative exponents indicating the reciprocal of the base raised to the positive exponent. Option number a is correct.
Step-by-step explanation:
To write the expression 512-4/3 with positive exponents, we need to recall the rule that says a negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent.
Therefore, the expression 512-4/3 becomes 1/5124/3. This means that we invert the base (512) and apply the positive exponent (4/3) to it. So the answer to the question is A. 1/5124/3.