simplification of squared expression

Question

I haven't done a math class in a while and I'm stumped on what seems to be a simple question.

How does

$$ ( [(k + 1)^2]/4 ) (k + 2)^2$$

simplify to $$ [ (k + 1)(k + 2)/2 ]^2 $$

What rule of simplifying exponents applies to this?

Answer 1

Step by step:

$$\frac{(k+1)^2}{4} \cdot (k+2)^2 = \frac{(k+1)^2}{2^2} \cdot (k+2)^2 = \left( \frac{k+1}{2} \right)^2 \cdot (k+2)^2 = \left( \frac{k+1}{2} \cdot (k+2) \right)^2 = \left( \frac{(k+1)(k+2)}{2} \right)^2$$

Do you understand what happens in each step?