We have a random triangle with base x, and height x - 5. Remember, the area of a triangle is base*height / 2, in this case base*height = 84.
Plugging in the values, we have (x)(x - 5) = 84. Opening parenthesis we have \(x^2 - 5x = 84\). Factoring we have (x - 12)(x + 7) = 0
Taking the positive value of x from -7 and 12, we have x = 12. Meaning that the height is 7.
Thus, the base = 12 units, the height = 7 units.
So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1. (src = scienceline.org)
0^1 is 0 because anything to the power of 1 is itself (since the 1 means how many times, 1 time is just the number given). Thus 0^1 is the base number, in which is 0.