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The LaTeX command for caret (^) is \textasciicircum.
\textasciicircumWrite \textasciicircum inside math mode — that is, between $…$ for inline math or in a \[ … \] / equation block for display math. It is part of core LaTeX math, so no extra package is required.
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Use \textasciicircum in math mode — it needs no extra package. For example, $\textasciicircum$.
None — \textasciicircum is built into LaTeX's math mode, so no extra package is required.