Calculating the Value of P in the Equation (2744)^(1/3) = 2p 2

To determine the value of p in the given equation, we need to apply the rules of exponentiation and solve step by step. Let's break down the process:

1. Understand the Notation
The notation (2744)^(1/3) represents the cube root of 2744. In other words, we need to find the number that, when multiplied by itself three times, equals 2744.

2. Calculate the Cube Root of 2744
The cube root of 2744 can be found by finding the number that, when multiplied by itself three times, equals 2744. Mathematically, we can express this as:
(2744)^(1/3) = p

To simplify the calculation, we can note that 2744 is equal to 14^3 (14 raised to the power of 3), as 14 * 14 * 14 = 2744.

Therefore, we can rewrite the equation as:
(14^3)^(1/3) = p

3. Apply the Rule of Exponentiation
The rule of exponentiation states that when an exponent is raised to another exponent, we multiply the exponents. Therefore, we can simplify the equation as follows:
14^(3*(1/3)) = p

The exponent 3*(1/3) can be simplified to 1, so our equation becomes:
14^1 = p

4. Solve for P
We know that any number raised to the power of 1 is equal to the number itself. Therefore, p is equal to 14.

Conclusion
In the given equation (2744)^(1/3) = 2p 2, the value of p is 14. By applying the rules of exponentiation, we simplified the equation to 14^1 = p, which means p is equal to 14.