1. Given data

• Mass of particle:
  $m = 10\text{ g} = 0.01\text{ kg}$
• Retardation:
  $a = -2x$ since retardation means acceleration opposite to motion.

2. Find the retarding force

Using Newton's second law, $F = ma = 0.01(-2x) = -0.02x$

So, the magnitude of retarding force is $|F| = 0.02x$

3. Loss of kinetic energy

By work-energy theorem, change in kinetic energy equals work done by force: $\Delta K = W = \int_0^x F\,dx$

Since the force is retarding, kinetic energy decreases. Thus loss of kinetic energy is the positive value: $\text{Loss in K.E.} = -\int_0^x F\,dx$

Now, $\int_0^x F\,dx = \int_0^x (-0.02x)\,dx$

Using a dummy variable $s$ for integration, $W = \int_0^x (-0.02s)\,ds = -0.02\left[\frac{s^2}{2}\right]_0^x$ $W = -0.01x^2$

Hence, $\text{Loss in K.E.} = 0.01x^2$

4. Match with the given form

Given: $\text{Loss in K.E.} = \left(\frac{10}{x}\right)^{-n}$

Now, $\left(\frac{10}{x}\right)^{-n} = \left(\frac{x}{10}\right)^n = \frac{x^n}{10^n}$

We found $\text{Loss in K.E.} = 0.01x^2 = \frac{x^2}{100} = \frac{x^2}{10^2}$

Comparing, $n=2$

5. Final answer

$\boxed{2}$