This conflicts with the 3^ cage in the leftmost column, which must be (1,1,3) with 3 in the corner.\
Here is where you go wrong. Since exponentiation is done from right to left, that cage can also be something like (1,3,7), since 3^(1^7)=3^1=3. In fact, any combination with both a 1 and a 3 is necessary and sufficient.
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