A correct solutions was received from Jared Abry, Bader Al-Kandari.  Correct solutions from outside the Bradley University community were received from Ahmed AboAdham, Iñigo Picaza, Chioma Odigwe, Juan Carlos Marivela, Bill Webb, Paul Botham, Juan Carlos Carrara, Dan Dima, Paul Lee, Gary Smith

The slope of the tangent line at the point (a,aⁿ) is na^n-1, and so the slope of the perpendicular is -1/na^n-1. The equation of the perpendicular is y - aⁿ = (x - a)/na^n-1 and the y-intercept of this line is at P(a) = aⁿ + 1/na^n-2.  So,

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