2^{7} + 2^{7} = 2^{8} (2^{7} = 128; 128 + 128 = 256; log_{2}256 = 8)

2^{10} + 2^{10} = 2^{11} (2^{10} = 1,024; 1,024 + 1,024 = 2,048; log_{2}2,048 = 11)

2^{24} + 2^{24} = 2^{25} (2^{24} = 16,777,216; 16,777,216 + 16,777,216 = 33,554,432; log_{2}33,554,432 = 25)

2^{½} + 2^{½} = 2^{3/2} (2^{½} = 1.4142...(the square root of 2); the square root of 2 *doubled* is the square root of 8; log_{2}2.8284...(the square root of 8)= 3/2 or 1½)

2^{-1} + 2^{-1} = 2^{0} (2^{-1} = ½; ½ + ½ = 1; log_{2}1 = 0)

2^{-2} + 2^{-2} = 2^{-1} (2^{-2} = ¼; ¼ + ¼ = ½; log_{2}½ = -1)

As you can see, even if ** x** is a non-integer or negative, it still works out! Even imaginary/complex powers work out in this math trick!

2^{i} + 2^{i} = 2^{1+i} (This statement is __true__ but 2^{i} & 2^{1+i} are both equal to irrational complex numbers, so I would have to type too many random digits!)

If you have a graphing calculator that can work with imaginary numbers, then you can see what those irrational complex numbers are.

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© Derek Cumberbatch