How does one raise one's self?

Calculus Level 1

11=122=433=2744=25655=3125\begin{aligned} 1^1 &=& 1 \\ 2^2 &=& 4 \\ 3^3 &=& 27 \\ 4^4 &=& 256 \\ 5^5 &=& 3125 \end{aligned}

Victoria just started learning about exponentiation in class, and she has written down the 5 equations above. She then postulates that

xxx^x is a strictly increasing function for positive xx.

Is her claim correct?

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