Let's simplify each expression step-by-step by applying exponent rules. Here are the main rules we'll use:

1. $(\frac{a}{b})^n = \frac{a^n}{b^n}$
2. $(a^m)^n = a^{m \cdot n}$
3. $(a \cdot b)^n = a^n \cdot b^n$

I'll start with the first few problems to provide a foundation. Let me know if you'd like detailed solutions for each individual question.

Solutions:

1. $\left(\frac{b}{h}\right)^3$: $= \frac{b^3}{h^3}$

2. $\left(\frac{2}{c^2}\right)^2$: $= \frac{2^2}{(c^2)^2} = \frac{4}{c^4}$

3. $\left(\frac{rq}{ds}\right)^5$: $= \frac{(rq)^5}{(ds)^5} = \frac{r^5 q^5}{d^5 s^5}$

4. $\left(\frac{ab}{cd}\right)^6$: $= \frac{(ab)^6}{(cd)^6} = \frac{a^6 b^6}{c^6 d^6}$

5. $\left(\frac{abc}{xyz}\right)^8$: $= \frac{(abc)^8}{(xyz)^8} = \frac{a^8 b^8 c^8}{x^8 y^8 z^8}$

6. $\left(\frac{x^2 y^3 z}{a^5 b^4 c^2}\right)^6$: $= \frac{(x^2 y^3 z)^6}{(a^5 b^4 c^2)^6} = \frac{x^{12} y^{18} z^6}{a^{30} b^{24} c^{12}}$

Would you like me to continue solving the rest of these questions, or do you need clarification on any specific one?

Additional Practice Questions:

1. Simplify $\left(\frac{p}{q^2}\right)^4$.
2. Expand and simplify $(a^2 b^3 c)^5$.
3. Write $\left(\frac{m^3}{n^4}\right)^2$ in simplest form.
4. Simplify $\left(\frac{x y^2}{z^3}\right)^3$.
5. Evaluate $\left(\frac{5a^2}{3b^3}\right)^2$.

Tip:

When simplifying expressions with exponents, remember to distribute the power to both the numerator and the denominator separately.