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I am trying to understand why $1^{x}=1$ for any $x\in\mathbb{R}$

Is it OK to write $1^{x}$? As the base 1 should not equal 1 for $1^{x}$ to be an exponential function?

Is $1^{x}=1$ just because it is defined to be so?

If possible please refer me to a book or article that discusses this topic.

3 Answers 3