Question

square solar panel has an area of 16 square feet. write the area as a power. then find the side lengths of the panel. the area of the solar panel written as a power is \boxed{} square feet. the side lengths of the solar panel are \boxed{4} feet.

Explanation:

Step1: Express 16 as a power

We know that \(16 = 4\times4=4^{2}\) or \(16 = 2\times2\times2\times2 = 2^{4}\). But since the side length is 4 (as the area of a square is \(s^{2}\), and if area is 16, \(s=\sqrt{16} = 4\)), the most relevant power for the area (related to the side length) is \(4^{2}\) or \(2^{4}\), but \(16=4^{2}\) is more direct here as the side length is 4. So the area as a power is \(4^{2}\) (or \(2^{4}\), but \(4^{2}\) is better in this context).

Step2: Confirm the power representation

The area of the square solar panel is 16 square feet. We can write 16 as \(4^{2}\) because the side length \(s = 4\) and area of square \(A=s^{2}\), so \(A = 4^{2}\).

Answer:

The area of the solar panel written as a power is \(4^{2}\) (or \(2^{4}\), but \(4^{2}\) is the most appropriate here) square feet. And the side length is 4 feet (which is correct as \(\sqrt{16}=4\)). For the power - filled box, the answer is \(4^{2}\) (or \(2^{4}\), but \(4^{2}\) is better). So the value to fill in the first box is \(4^{2}\) (or \(2^{4}\), but we'll use \(4^{2}\) as the side length is 4).