I see that you've uploaded a math exercise image. Let's break down and solve the highlighted problems one by one:

1. Problem 2(a): $(2a)^4$

• Apply the power of a product rule: $(ab)^n = a^n \cdot b^n$. $(2a)^4 = 2^4 \cdot a^4 = 16a^4$ Answer: $16a^4$

2. Problem 4(a): $(r^3)^3$

• Apply the power of a power rule: $(a^m)^n = a^{m \cdot n}$. $(r^3)^3 = r^{3 \cdot 3} = r^9$ Answer: $r^9$

3. Problem 5(a): $(-2ac)^2$

• Apply the power of a product rule again: $(ab)^n = a^n \cdot b^n$. $(-2ac)^2 = (-2)^2 \cdot a^2 \cdot c^2 = 4a^2c^2$ Answer: $4a^2c^2$

4. Problem 8(a): $\left(\frac{-2s}{u^3}\right)^2$

• Apply the power to both the numerator and the denominator. $\left(\frac{-2s}{u^3}\right)^2 = \frac{(-2)^2 \cdot s^2}{(u^3)^2} = \frac{4s^2}{u^6}$ Answer: $\frac{4s^2}{u^6}$

5. Problem 12(a): $(a^2 \cdot a)^3$

• Simplify the expression first by combining like terms: $a^2 \cdot a = a^3$.
• Now apply the power of a power rule: $(a^3)^3 = a^{3 \cdot 3} = a^9$. Answer: $a^9$

Would you like more detailed explanations on any of these, or do you have additional questions?

Here are 5 related questions to expand on these concepts:

1. How do you simplify expressions involving multiple variables with exponents?
2. What happens when negative bases are raised to even powers?
3. Can you explain the difference between applying the power of a power rule and power of a product rule?
4. How would you simplify the expression $(xy)^4$?
5. How do you simplify fractional exponents such as $(a^{3/2})^2$?

Tip: Always remember to first simplify inside parentheses before applying any exponent rules.