Question Video: Using a Zero Exponent to Deduce Whether a Statement is True | Nagwa Question Video: Using a Zero Exponent to Deduce Whether a Statement is True | Nagwa

# Question Video: Using a Zero Exponent to Deduce Whether a Statement is True Mathematics

True or False: (𝑥 + 𝑦)⁰ = 𝑥⁰ + 𝑦⁰, where 𝑥 + 𝑦 ≠ 0, 𝑥 ≠ 0, and 𝑦 ≠ 0.

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### Video Transcript

True or false: 𝑥 plus 𝑦 to the power of zero is equal to 𝑥 to the power of zero plus 𝑦 to the power of zero, where 𝑥 plus 𝑦 is not equal to zero, 𝑥 is not equal to zero, and 𝑦 is not equal to zero.

We know that for any nonzero 𝑥, 𝑥 to the power of zero is equal to one. We are told that 𝑥 plus 𝑦 is not equal to zero. This means that raising this to the power of zero will give us an answer of one. On the right-hand side of the equation, we have 𝑥 to the power of zero plus 𝑦 to the power of zero. Both of these terms will be equal to one. This means that 𝑥 to the power of zero plus 𝑦 to the power of zero is equal to two. As the left-hand side is not equal to the right-hand side, the statement 𝑥 plus 𝑦 to the power of zero equals 𝑥 to the power of zero plus 𝑦 to the power of zero is false.

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