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The task requires simplification of the given expressions. Let's go through each one step-by-step:

### Given expressions:

1. **(a) \( 2a^2 \cdot 3a^3 \)**
   - Simplify: Multiply the coefficients and add the exponents of like terms.
   - Solution: \( 6a^{2+3} = 6a^5 \).

2. **(b) \( 0.5b^5 \cdot 4b^2 \)**
   - Simplify: Multiply the coefficients and add the exponents of like terms.
   - Solution: \( 2b^{5+2} = 2b^7 \).

3. **(c) \( \frac{2}{3}b^3 - 3b^4 \)**
   - Simplify: This expression is already simplified since there are no like terms to combine.
   - Solution: \( \frac{2}{3}b^3 - 3b^4 \).

4. **(d) \( \frac{2}{3}(a^3)^5 \cdot 7a^3 \)**
   - Simplify: Use the power rule \((a^m)^n = a^{mn}\), then multiply the coefficients and add exponents.
   - Solution: \( \frac{2}{3}a^{15} \cdot 7a^3 = \frac{14}{3}a^{18} \).

5. **(e) \( -3.6a^4 \cdot \frac{1}{3}b^2 \)**
   - Simplify: Multiply the coefficients and write the expression in standard form.
   - Solution: \( -1.2a^4b^2 \).

6. **(f) \( -12a^5 - \frac{1}{11}a^5 \)**
   - Simplify: Combine the like terms.
   - Solution: \( -\frac{133}{11}a^5 \).

7. **(g) \( \frac{3.5b^6}{0.5b^2} + 3b \)**
   - Simplify: Divide the terms and add the remaining expression.
   - Solution: \( 7b^4 + 3b \).

8. **(h) \( \left( \frac{1}{4}b \right)^{-3} \cdot \frac{1}{16}b^4 + 2b \)**
   - Simplify: Use the property of exponents \(\left( \frac{1}{a} \right)^{-n} = a^n\), then add the expressions.
   - Solution: \( 64b^3 + \frac{1}{16}b^4 + 2b \).

Would you like more details on any of these steps, or have any questions?

### Related questions:
1. How do you apply the power rule when multiplying expressions with exponents?
2. What steps should be followed to combine like terms in polynomial expressions?
3. How do you simplify expressions with negative exponents?
4. What are the rules for multiplying and dividing fractions involving variables?
5. How do you handle expressions with mixed coefficients (decimals and fractions)?

**Tip:** Always arrange terms in descending order of their exponents for clarity when simplifying algebraic expressions.

Simplify the algebraic expressions given in the image.

Simplify algebraic expressions involving exponents, coefficients, and like terms. This includes applying the laws of exponents and combining terms. Suitable for students in Grades 8-10.

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