This (and your other cases) are using more multiplications than necessary. For example, x^8 = ((x*x)^2)^2, which is only 3 multiplications instead of 7. You can do return @fastpow x^8 here (or return @fastmath x^8 for hardware-float types), I guess.
But I agree with @Oscar_Smith that it’s better to optimize the larger context for these calculations.