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For the equation "If y^a × y^b = 1 and y ≠ ± 1, then a + b =," please show your solution with 4 points.

User JamesDS
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1 Answer

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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.

User Conrad Irwin
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