Here are the answers to your questions:
Question 1: Choose the correct simplification of the expression \( (8x^2)^3 \).
Correct Answer: 512x^6
Question 2: Simplify \( (3xy^2)(4xy)(2xy)^3 \).
Correct Answer: 96x^5y^6
Question 3: Choose the correct simplification of \( \frac{m^7n^4}{m^4n^3} \).
Correct Answer: m^3n
Question 4: Choose the correct simplification of the expression \( (a^2)^3 \).
Correct Answer: a^6
Question 5: Choose the correct simplification of \( (2x)(4y) \).
Correct Answer: 8xy
Question 6: Choose the correct simplification of the expression \( c^2 \cdot c^9 \).
Correct Answer: c^{11}
Question 7: Choose the correct simplification of the expression \( 2 \cdot \frac{b}{c} \) all to the power of 3.
Correct Answer: \frac{8b^3}{c^3}
Question 8: Choose the correct simplification of \( (7x^3y^3)^2 \).
Correct Answer: 49x^6y^6
Question 9: Choose the correct simplification of the expression \( \frac{16}{n^{-3}} \).
Correct Answer: \frac{n^3}{16}
Question 10: Choose the correct simplification of \( (xy^2z)^3 \).
Correct Answer: x^3y^6z^3
Please review them and let me know if you have any further questions!