Final answer:
The query provides an examination of mathematical problems ranging from multiplicative adjustments in scientific notation to factorial calculation, rules of exponentiation, and operations with powers of ten.
Step-by-step explanation:
The question seems to explore various mathematical concepts including multiplication, exponentiation, and division with powers of ten. Specifically, it touches on the method of changing the format of a number by adjusting the prefactor and exponent which is a common technique used in scientific notation. This concept is exemplified when the number 24 is multiplied by 10¹ to make calculations easier, ultimately revealing that math can offer multiple pathways to the same solution. Additionally, the importance of understanding factorials and the rules for combining exponents, such as (x⁺)² = x⁺∗², is highlighted. Moreover, the question delves into division within scientific notation, like 2.4 × 10¹ divided by 8 × 10⁷, and straightforward arithmetic operations, such as adding or multiplying whole numbers.