If x^y is equivalent to y 2 – x, what is the value of y^(y^y)?

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The definition of the function states that the term before the ^ symbol should be squared and the term after the ^ symbol should be subtracted from that square. Begin with the innermost function: y^y: Square the second term, y, and subtract the first term, y: y 2 – y. Now evaluate y^(y 2 – y). Again, square the second term, y 2 – y, and subtract the first term, y: (y 2 – y) 2 – y = y 4 – y 3 – y 3 + y 2 – y = y 4 – 2y 3 + y 2 – y.

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