Is the set of irrational numbers closed under the operation of exponentiation? That is, for all irrational numbers a and b, is a^b irrational? Why?
Consider $\displaystyle e^{\ ln A} = A$. if $\displaystyle A$ is a rational number than$\displaystyle \ln A$ is irrational. So here you have an example of an irrational number raised to an irrational number yielding a rational number result.