Final answer:
This question involves concepts from high school level mathematics, focusing on the basic arithmetic operations with positive and negative numbers, rules for signs during multiplication and division, and working with exponents, including negative exponents and scientific notation.
Step-by-step explanation:
The student's query pertains to several mathematical operations such as addition, subtraction, multiplication, division, and working with exponents. These operations also include the application of rules concerning the signs of numbers when they are manipulated through these operations. For example, subtracting a positive number (e.g., 5-(+3)), where 3 is subtracted from 5 resulting in 2. In subtraction, if the second number is negative, it turns into addition (e.g., 2-(-6)=2+6 = 8). In multiplication, like signs result in a positive product (e.g., (-4) x (-3) = 12) and unlike signs result in a negative product (e.g., 4 x (-4) = -16). Division follows the same sign rules as multiplication. Concepts of negative exponents and their relation to fractions are also covered, e.g., x^(-n) = 1/(x^n). Additionally, working with scientific notation is covered, such as dividing numbers by subtracting their exponents (e.g., 10^6 / 10^2 = 10^(6-2) = 10^4).