Final answer:
The value of x that satisfies the equation (72) to the power of x = 1 is x = 0. This is because any non-zero number raised to the zero power equals the multiplicative identity, which is 1.
Step-by-step explanation:
When given the equation (72) to the power of x = 1, we need to identify the value of x that makes this statement true. In Mathematics, there is a rule that any non-zero number raised to the power of zero is equal to 1. This is because the exponent zero signifies that there are zero instances of the number being multiplied together, which leaves us with the multiplicative identity, which is 1.
Therefore, the value of x that satisfies the equation (72)^x = 1 is x = 0. This is due to the fact that 72 raised to the power of zero is 1, which adheres to the fundamental rule that anything to the zero power equals 1. No other exponent will result in the base of 72 giving us a product of 1 except for 0.