Easy exponentiation method Is there a simple way of solving, say, $x^{3/2}$?
For example, one way of solving $16^{3/2}$ is to calculate the square root of $16^3$, but I was wondering if there is a simpler mental trick for doing this that generalizes to all possible exponentiation.

Following Troy Woo and Travis comments, let us make it more general : you want to know $x$ such that $$x^a=b$$ and you know already a solution for a given $a$ and a value close to $b$.
Newton method is quite simple since, starting at your known estimate $x_0$, the first iterate will be $$x_1=x_0-\frac{x_0^{1-a} \left(x_0^a-b\right)}{a}$$
Let us apply it to $a=\frac{3}{2}$, $b=10$ and $x_0=4$. This gives $$x_1=\frac{14}{3} \simeq 4.66667$$ while the exact solution is $4.64159$
