Final answer:
The product abcd is defined by the equation abcd = 2(a²b²c²d²), meaning the product will always be twice the square of real numbers. When this guideline is applied to the numbers 50, 100, 200, 450, and 800, only 450 results in a non-real number, indicating it cannot be expressed as the product abcd.
Step-by-step explanation:
The initial property provided can be rewritten as abcd = 2(abcd)², which simplifies to abcd = 2(a²b²c²d²). In terms of this equation, we want to find a number that cannot be expressed as the output of this equation.
We can test the potential outputs provided: 50, 100, 200, 450, and 800. Plugging in these values on the right-hand side of the equation, we'd notice that the square root of each number divided by the square root of 2 (which are all real numbers) could theoretically be the value of ab or cd, which means that 50, 100, 200, and 800 all could be expressed as the product abcd according to the properties of the equation.
However, 450, when divided by the square root of 2, results in a non-real number when you try to take the square root, meaning that 450 cannot be expressed as the product abcd.
Learn more about Number properties