solve path: the multiplication by 6 implies 1-down must be 00 or 01. try both possibilities. either way, the highlighted digit becomes 0, from there, there are only 2 possibilities and it can be shown that 1-down = 1 does not work by 3-across.
also a small nitpick, 0^0 is undefined. still, great use of almost 3 minutes. made me laugh for sure
Count me as a fail because I’m use to having 0^0 being undefined. The reason for this is that 0^x 0 as x approaches 0 but x^0 1 as x approaches 0. Since either makes sense for 0^0 it is often left undefined. This led me to no valid solutions being possible and I gave up. That said, I am very happy to have inspired evil!. Welcome to the Terrordome!
I will grant that it is not certainly not incorrect. For anyone following along at home, here is a good video explaining both points of view: https://m.youtube.com/watch?v=4Hm4fMkl5XI. In my work, 0^0 comes out of calculus limits, and this is best left undefined. In other fields, such as combinatorics, 0^0 is best taken as 1. I give @TheNoah a +0^0 for this puzzle!
Sorry to have wasted your time. I see that frustrated a lot of people. If I was doing the bit again I would only have subtraction and multiplication clues.
0 as x approaches 0 but x^0 
glad you had zero fun.