Final answer:
To simplify the expression (8a^3÷27x^-3)1÷3, divide the numbers inside the parentheses and simplify the exponents. Then, raise the simplified expression to the power of 1/3 and multiply the exponents. Finally, divide the resulting terms to get the simplified expression 2a/(9x).
Step-by-step explanation:
To simplify the expression (8a^3÷27x^-3)1÷3, we can start by simplifying inside the parentheses. First, divide 8a^3 by 27 to get (8/27)a^3. Then, divide x^-3 by 27 to get 1/(27x^3). Next, simplify 1/3 to get 1/3. Now, when we raise (8/27)a^3 to the power of 1/3, and (1/(27x^3)) to the power of 1/3, we can multiply the exponents inside the parentheses. So, (8/27)a^3 raised to the power of 1/3 becomes (8/27)^(1/3)a^(3/3), which simplifies to (2/3)a. And, (1/(27x^3)) raised to the power of 1/3 becomes (1/27x^3)^(1/3), which simplifies to 1/(3x). Therefore, the simplified expression is (2/3)a divided by (3x), which can also be written as 2a/(9x).