Final answer:
To solve the given equation y^a × y^b = 1 where y ≠ ± 1, we add the exponents due to the multiplication of like bases, which gives y^(a+b) = 1. Since y ≠ ± 1, a + b must equal zero for the equation to hold true.
Step-by-step explanation:
To solve the equation y^a × y^b = 1 where y ≠ ± 1, we can use the properties of exponents. Specifically, recall that when we multiply like bases, we add their exponents.
So, the equation becomes: y^(a+b) = 1.
Since y ≠ ± 1, the only way for y raised to any power to equal 1 is if that power is zero (because any non-zero number to the power of zero equals one). Therefore, we can deduce that: a + b = 0.