(a) \(2^{\frac{n}{2}}\)
In the G.P, 1, 2, 22, ....., 2n, there are (n + 1) terms.
∴ Geometric mean of this G.P. = (1 x 2 x 22 x ... x 2n)\(\frac{1}{n+1}\)
= \((2^{1+2+3+....+n})^{\frac{1}{n+1}}\)
= \(\big(2^{\frac{n}{2}(n+1)}\big)^{\frac{1}{n+1}}\) = \(2^{\frac{n}{2}}\).