1. The quantity is given by

$Q = X^{-2} Y^{3/2} Z^{-2/5}$

2. For a quantity of the form

$Q = X^a Y^b Z^c$

the maximum fractional error is

$\frac{\Delta Q}{Q} = |a|\frac{\Delta X}{X} + |b|\frac{\Delta Y}{Y} + |c|\frac{\Delta Z}{Z}$

We take absolute values of the powers because errors always add in magnitude for maximum error.

3. Given:

$\frac{\Delta X}{X} = 0.1, \qquad \frac{\Delta Y}{Y} = 0.2, \qquad \frac{\Delta Z}{Z} = 0.5$

and powers are:

$a=-2, \quad b=\frac{3}{2}, \quad c=-\frac{2}{5}$

4. Substitute into the formula:

$\frac{\Delta Q}{Q} = |-2|(0.1) + \left|\frac{3}{2}\right|(0.2) + \left| -\frac{2}{5} \right|(0.5)$

$= 2(0.1) + \frac{3}{2}(0.2) + \frac{2}{5}(0.5)$

5. Calculate each term:

$2(0.1)=0.2$

$\frac{3}{2}(0.2)=0.3$

$\frac{2}{5}(0.5)=0.2$

6. Add them:

$\frac{\Delta Q}{Q} = 0.2 + 0.3 + 0.2 = 0.7$

7. Therefore, the maximum fractional error is

$\boxed{0.7}$

So the correct option is C.