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The exercise sheet titled "Übungsaufgaben zu Potenzen und Wurzeln" contains a series of problems related to exponents (powers) and roots. Here is a breakdown of the types of problems presented:

1. **Convert to Positive Exponents**:
   Rewrite each expression so that all exponents are positive. This involves applying the rule:  
   \( x^{-n} = \frac{1}{x^n} \).

2. **Simplify Using the Laws of Exponents**:
   Apply the properties of exponents, such as the multiplication and division of powers:
   - \( x^m \cdot x^n = x^{m+n} \)
   - \( \left( x^m \right)^n = x^{mn} \)
   - \( \frac{x^m}{x^n} = x^{m-n} \)

3. **Simplify/Write as a Single Power**:
   Combine the terms into a single exponent by multiplying or dividing powers with the same base.

4. **Simplify as Much as Possible**:
   These are more complex expressions that require applying multiple exponent rules to simplify completely.

5. **Write as a Root or Power**:
   Convert fractional exponents into roots (e.g., \( x^{1/2} = \sqrt{x} \)).

6. **Simplify**:
   Simplify expressions involving roots and exponents by applying square root and power rules.

### Would you like me to walk through specific solutions to these problems?

In the meantime, here are five related questions for practice:

1. How do you simplify \( x^{-3} \cdot x^5 \)?
2. What is the result of \( (2a^2)^3 \)?
3. How do you express \( \frac{1}{y^2} \) as a power with a negative exponent?
4. What are the steps to simplify \( \frac{a^5}{a^2} \)?
5. How do you simplify \( \sqrt[3]{x^6} \)?

**Tip:** Always remember that fractional exponents represent roots, and negative exponents represent reciprocal powers.

This worksheet contains problems on exponents and roots. It covers simplifying exponents, converting to positive exponents, applying exponent rules, and converting between powers and roots. Ideal for Grades 8-10 students studying algebra.

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