Raise a number to the "y" power without using exponents.

Question

This is kind of a spinoff on my question Divide by a number without dividing.

Can anyone think of some clever ways to raise any given number to any given power without using an exponent anywhere in your equation/formula?

$$x^{y}=z$$

Answer 1

You can always use the Taylor series for $f(u) = e^u$.

$$ x^y = 1 + y \ln x + \frac{(y \ln x)(y \ln x)}{2!} + \frac{(y \ln x)(y \ln x)(y \ln x)}{3!} + \cdots $$