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For example, x=1, y=2, it is 1², how to read the expression?

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There are several ways to read mathematical expressions. For powers, you could say:

x raised to y

x raised to the power of y

x raised to the yth power

[...]

If you're raising the number to 2 or 3, say x "squared" or "cubed" respectively. You could use any one of the above, as long as the listeners know the context is mathematical.