**64/125 to the Power of 2/3: A Mathematical Exploration**

In this article, we will delve into the world of exponentiation and explore the result of raising the fraction 64/125 to the power of 2/3.

**What is Exponentiation?**

Exponentiation is a mathematical operation that involves raising a number or an expression to a power. It is denoted by a superscript number or symbol, which indicates the power to which the base number or expression should be raised. For example, 2^3 means 2 to the power of 3, which is equivalent to 2 × 2 × 2 = 8.

**The Fraction 64/125**

The fraction 64/125 is a rational number that can be simplified to 16/25. This fraction represents a part of a whole, where 64 is the numerator and 125 is the denominator.

**Raising 64/125 to the Power of 2/3**

Now, let's explore what happens when we raise the fraction 64/125 to the power of 2/3.

**(64/125)^(2/3)**

To evaluate this expression, we need to follow the rules of exponentiation. Since the exponent is a fraction, we can rewrite it as:

**(64/125)^(2/3) = (64^(2/3))/(125^(2/3))**

Using the rules of exponentiation, we can simplify this expression further:

**(64^(2/3))/(125^(2/3)) = ((64^2)^(1/3))/((125^2)^(1/3))**

Evaluating the numerator and denominator separately, we get:

**(64^2)^(1/3) = (4096)^(1/3) = 16**

**((125^2)^(1/3)) = (15625)^(1/3) = 25**

Now, we can simplify the original expression:

**(64/125)^(2/3) = 16/25**

**What Does This Result Mean?**

The result of raising 64/125 to the power of 2/3 is equal to 16/25. This means that if we start with the fraction 64/125 and raise it to the power of 2/3, we will get a new fraction that is equivalent to 16/25.

**Conclusion**

In this article, we explored the result of raising the fraction 64/125 to the power of 2/3. By applying the rules of exponentiation, we were able to simplify the expression and arrive at a new fraction, 16/25. This exercise demonstrates the beauty and complexity of mathematical operations and highlights the importance of understanding exponentiation in mathematics.