Question 2: a) Express 216 as a product of prime factors. Hence evaluate (216)2/3. b) Solve the inequality 1/2(x+1) >= 1/3(2x+2) and illustrate the answer on a number line.

$$216 = 2 \times 108$$ $$108 = 2 \times 54$$ $$54 = 2 \times 27$$ $$27 = 3 \times 9$$ $$9 = 3 \times 3$$

So, $216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 2^3 \times 3^3$.
The product of prime factors is $\boxed{\textbf{2}^\textbf{3} \times \textbf{3}^\textbf{3}}$.

$$(2^3 \times 3^3)^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} \times (3^3)^{\frac{2}{3}}$$ $$= 2^{3 \times \frac{2}{3}} \times 3^{3 \times \frac{2}{3}}$$ $$= 2^2 \times 3^2$$ $$= 4 \times 9$$ $$= 36$$

The value is $\boxed{\textbf{36}}$.

$$6 \times \frac{1}{2}(x+1) \ge 6 \times \frac{1}{3}(2x+2)$$ $$3(x+1) \ge 2(2x+2)$$

Subtract $3x$ from both sides:

$$3 \ge 4x - 3x + 4$$ $$3 \ge x + 4$$

Subtract 4 from both sides:

$$3 - 4 \ge x$$ $$-1 \ge x$$

This can be rewritten as $x \le -1$.

The solution $x \le -1$ means all real numbers less than or equal to -1. This is represented by a closed circle at -1 and an arrow extending to the left.

$$\text{Number Line:} \quad \longleftarrow \bullet \text{--------------------} \\ \quad \quad \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1$$

The solution is $\boxed{\textbf{x} \le \textbf{-1}}$.