What is the best way to define 4 raised to the power of 2 over 3?

To understand the expression 4^2/3, we can break it down into more manageable parts.

Firstly, 4 can be expressed as 2² because 2 squared gives us 4. This means we can rewrite the entire expression:

4^2/3 = (2²)^2/3.

Next, when raising a power to another power, we multiply the exponents:

(2²)^2/3 = 2^{(2 * 2/3)} = 2^4/3.

The resulting expression, 2^4/3, can be interpreted in two key ways:

1. It represents the cube root of 2 raised to the power of 4, which can be written as:

2^4/3 = 2⁴ (cube root)

2. Alternatively, you could also express it as:

(cube root of 2)⁴.

In conclusion, 4^2/3 is best defined as 2^4/3, which can be interpreted either as analyzing the cube root of 2 raised to the fourth power or as the fourth power of the cube root of 2. Understanding this notation helps us work with exponents more effectively and reveals the versatility within mathematical expressions.