Simplifying (64/27)^(1/3)
This expression involves both fractional exponents and negative exponents. Let's break it down step by step:
Understanding Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. In other words:
 x^n = 1/x^n
Understanding Fractional Exponents
A fractional exponent represents a root. The denominator of the fraction indicates the type of root. For example:
 x^(1/n) = nth root of x
Applying the Rules

Reciprocal: First, we address the negative exponent. (64/27)^(1/3) becomes (27/64)^(1/3).

Cube Root: Now we deal with the fractional exponent. (27/64)^(1/3) is the cube root of (27/64).

Calculation: The cube root of 27 is 3, and the cube root of 64 is 4. Therefore, the simplified answer is 3/4.
In Conclusion
(64/27)^(1/3) simplifies to 3/4. By applying the rules of exponents, we were able to break down the expression and arrive at a simple numerical answer.