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.
