Final answer:
The product of powers of nine obeys the rule of adding exponents when the base is the same. In a Cartesian coordinate system, the scalar products of orthogonal unit vectors are zero. In genetics, the 9:3:3:1 phenotypic ratio is a result of Mendel's law of independent assortment.
Step-by-step explanation:
The product of powers of nine follows a specific mathematical rule which is a case of the general rule for multiplying powers with the same base. The rule states that when multiplying powers with the same base, you add the exponents. In the given example, when we calculate 32 × 35, we simply add the exponents 2 + 5 to get 37.
This can be understood as 32 × 35 = 3(2+5) = 37.
Another part of the question references a Cartesian coordinate system where the scalar products of orthogonal unit vectors result in zero because the cosine of 90° is zero. This implies that in such a system, any two perpendicular directions, such as the eastward and northward directions, do not influence each other.
Finally, discussing the concept of independent assortment in genetics, the 9:3:3:1 dihybrid phenotypic ratio is explained. It is related to Mendel's law of independent assortment, which states that alleles for different traits are distributed to sex cells (gametes) independently of one another. This results in the mentioned phenotype ratios among offspring.