To understand what 4 to the power of 2 over 3 means, we first need to break it down into simpler parts. The expression can be written mathematically as 4^(2/3).
This expression involves two operations: exponentiation and the concept of a root. The 2 in the exponent signifies that we will first square 4, and the 3 in the denominator of the exponent indicates we will then take the cube root of the result.
Let’s compute it step by step:
1. First, calculate 4 squared:
4^2 = 16
2. Next, take the cube root of 16:
The cube root of 16 is the value that, when multiplied by itself three times, equals 16. This is not a whole number, but it can be approximated.
Mathematically, this can be expressed as 16^(1/3), and its approximate value is around 2.52.
In conclusion, 4 to the power of 2 over 3 is best defined as the cube root of 16, which can be calculated as approximately 2.52.