Let’s solve the problems step-by-step.

Problem (g)

The expression is: $100^{0.1} : 100^{0.6}$

In terms of exponents, division of powers with the same base $a^{m} : a^{n} = a^{m-n}$. Therefore: $100^{0.1} : 100^{0.6} = 100^{0.1 - 0.6} = 100^{-0.5}$

Now, rewrite $100^{-0.5}$ as: $100^{-0.5} = \frac{1}{100^{0.5}}$

Since $100^{0.5} = \sqrt{100} = 10$, we get: $\frac{1}{10} = 0.1$

So, the answer for (g) is: $0.1$

Problem (h)

The expression is: $81^{-\frac{2}{3}} : 81^{-\frac{11}{12}}$

Using the same rule for exponents: $81^{-\frac{2}{3}} : 81^{-\frac{11}{12}} = 81^{-\frac{2}{3} + \frac{11}{12}}$

To add the exponents, find a common denominator: [ -\frac{2}{3} = -\frac{8}{12} \quad \text{and} \quad -\frac{11}{12} = -\frac{8}{12} + \frac{11}{12} = \frac{3}{12}