If Planck's constant (h) , speed of light in vacuum (c) and...

The standard dimensional formulas of the given constants are:
Planck's constant, $h = [ML^2T^{-1}]$
Speed of light, $c = [LT^{-1}]$
Gravitational constant, $G = [M^{-1}L^3T^{-2}]$

Let us evaluate the dimensions of the given expression $[h^{1/2} c^{-5/2} G^{1/2}]$:
First, find the product $hG$:
$hG = [ML^2T^{-1}] \times [M^{-1}L^3T^{-2}] = [L^5T^{-3}]$

Now, raise it to the power of $1/2$:
$(hG)^{1/2} = [L^{5/2}T^{-3/2}]$

Next, evaluate $c^{-5/2}$:
$c^{-5/2} = [LT^{-1}]^{-5/2} = [L^{-5/2}T^{5/2}]$

Multiplying these terms together:
$[h^{1/2} c^{-5/2} G^{1/2}] = [L^{5/2}T^{-3/2}] \times [L^{-5/2}T^{5/2}]$
$= [L^{5/2 - 5/2} T^{-3/2 + 5/2}]$
$= [L^0 T^1] = [T]$

This is the dimensional formula of time.

Answer: Time