Answer:

1) To solve this problem, we need to find the ratio of the volume of a grain of rice to the volume of the box, and then multiply it by the number of grains in one cubic meter.

The volume of a grain of rice is 20^(-9) m³.

The volume of the box is 20^(-3) m³.

To find the ratio, we divide the volume of the box by the volume of a grain of rice:

Ratio = (20^(-3) m³) / (20^(-9) m³)

Simplifying this expression, we subtract the exponents:

Ratio = 20^(3-(-9)) = 20^(12) = 4.096 x 10^(12)

Now, we multiply this ratio by the number of grains in one cubic meter:

Number of grains = Ratio x (Number of grains in one cubic meter)

The number of grains in one cubic meter can vary, but a common estimate is around 50,000 to 80,000 grains. Let's use 70,000 grains as an example:

Number of grains = 4.096 x 10^(12) x 70,000

Number of grains = 2.8672 x 10^(17)

Therefore, there are approximately 2.8672 x 10^17 grains in the box.

2) To find the weight of the adult chicken, we need to multiply the weight of the newborn chicken by the given factor.

The weight of the newborn chicken is 3^(-2) grams.

The factor by which an adult hen weighs more than a newborn chicken is 3^(4).

To find the weight of the adult chicken, we multiply these two values:

Weight of adult chicken = (3^(-2) grams) x (3^(4))

Simplifying this expression, we add the exponents:

Weight of adult chicken = 3^(-2+4) grams = 3^(2) grams

Therefore, the weight of the adult chicken is 3^(2) grams, or 9 grams