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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.

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

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

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### 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.

Learn how to simplify algebraic expressions involving exponents in fractions. This guide provides step-by-step solutions for simplifying complex fractional exponents and powers, ideal for high school students.

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