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^ means, "to the exponent of"
The word "carat" (karat) has the homonyms (homophones) caret and carrot. CARET - the keyboard symbol (^) CARROT - a vegetable plant with an edible orange root
Ideally using a superscript 4 to the right of the thing being raised to the power of 4. Computer languages can use: 1) a double multiplication sign - a double asterisk, eg 2**4 is 2 to the power 4, which is 16; or 2) the caret symbol, eg 2^4 is 2 to the power 4. The latter (using the caret symbol) is often used when a superscript is impossible, outside computer languages.
It is used to indicate an exponent eg 2 squared can be expressed as 2^2
To my knowledge, there is no symbol used for quotients in mathematics.