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The image contains a set of algebraic problems asking for simplifications, factorizations, and operations involving powers and algebraic expressions. Here's a breakdown of the two main sections visible in the image:

### Section 4: **"Kürze soweit möglich" (Simplify as much as possible)**

**a) \( 12a b^2 \div 60ab \)**  
Simplify this expression by canceling out common factors.

**c) \( (0.5k + 2m)^2 \)**  
Expand this binomial using the formula \( (a + b)^2 = a^2 + 2ab + b^2 \).

**e) \( (x - 1)^5 \cdot (x - 1)^6 \)**  
Use the property of exponents \( a^m \cdot a^n = a^{m+n} \).

**g) \( 3k+2 \cdot 3 - 3k \)**  
Distribute and simplify.

### Section 5: **"Vereinfache" (Simplify)**

**a) \( x^2 y^2 \)**  
Simplify the product of powers.

**b) \( 10^6 \cdot 10^{-4} \)**  
Apply the rule \( a^m \cdot a^n = a^{m+n} \).

**c) \( x^7 \div x^{-2} \)**  
Use the exponent rule for division \( a^m \div a^n = a^{m-n} \).

**d) \( (a + 2b)^5 \div (a + 2b)^4 \)**  
Simplify using exponent properties.

**f) \( 9a^2 b^5 \div 1.5 a^3 b^{-2} \)**  
Simplify the powers of both \( a \) and \( b \).

Let me know which specific question you'd like to go through in more detail, or if you want all of them explained. Would you like the solutions to these problems?

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### Here are 5 questions based on this:

1. How do you apply exponent rules when multiplying or dividing powers with the same base?
2. What is the process of expanding a binomial using the square formula?
3. How can factoring help simplify algebraic expressions?
4. What are the steps to solve polynomial multiplication?
5. How do you simplify expressions involving both coefficients and variables raised to powers?

### Tip:
Always apply basic exponent rules like \( a^m \cdot a^n = a^{m+n} \) and \( a^m \div a^n = a^{m-n} \) when simplifying powers with the same base.

The image contains algebraic problems asking for simplification and operations involving exponents, multiplication, and division.

Learn how to simplify algebraic expressions involving exponents, polynomial multiplication, and basic factorization. This set of problems covers exponent rules, binomial expansion, and distribution, suitable for students in Grades 9-11.

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