Let's solve each of these problems step by step:

Problem 11:

$22^0 \cdot 22^4$ When multiplying exponents with the same base, we add the exponents: $22^{0 + 4} = 22^4$ Thus, the answer is $22^4$.

Problem 12:

$8^5 \cdot 8^{-6}$ Again, using the rule of adding exponents when the bases are the same: $8^{5 + (-6)} = 8^{-1}$ So, the answer is $8^{-1}$. If we want only positive exponents, we can rewrite it as: $\frac{1}{8}$

Problem 13:

$12^{-4} \cdot 12^{-7}$ Similar to previous steps: $12^{-4 + (-7)} = 12^{-11}$ So, the answer is $12^{-11}$. To use only positive exponents, it becomes: $\frac{1}{12^{11}}$

Problem 14:

$3w^{-9} \cdot w^4$ Using the same rule: $w^{-9 + 4} = w^{-5}$ Thus, the answer is: $3w^{-5}$ Rewriting with positive exponents: $\frac{3}{w^5}$

Problem 15:

$9h^{-2} \cdot 5h^{10}$ Here, we multiply the constants and add the exponents for the variable part: $(9 \cdot 5) \cdot h^{-2 + 10} = 45 \cdot h^8$ Thus, the answer is: $45h^8$

Problem 16:

$0.4m^{-2} \cdot 0.6m^{-9}$ We multiply the constants and add the exponents for the variable part: $(0.4 \cdot 0.6) \cdot m^{-2 + (-9)} = 0.24 \cdot m^{-11}$ So, the answer is: $0.24m^{-11}$ Rewriting with positive exponents: $\frac{0.24}{m^{11}}$

Would you like further explanations or additional details on any of these?

Here are some related questions for further practice:

1. What is the product of $7^3 \cdot 7^2$?
2. How would you simplify $5x^{-3} \cdot x^7$?
3. What is the result of $3^0 \cdot 3^5$?
4. Simplify $4y^2 \cdot y^{-4}$.
5. How would you write $\frac{2^3}{2^6}$ using positive exponents?

Tip: When multiplying exponents with the same base, always add the exponents!