For which x value would the graph of y =x^6-25 be below the x-axis?

If you want the point to be located below the axis, then that would be located in the 3rd or 4th quadrant. In this case, the y-coordinate may be negative. TO be able to determine that, let's find x first when y will be zero.

y = x⁶ - 25
x⁶ = 25
x = (25)^(1/6) = 1.71

Therefore, the point will be anywhere below the x-axis if x is less than 1.71 (x < 1.71).