Final answer:
This explanation covers basic arithmetic rules involving the addition, subtraction, multiplication, and division of numbers with different signs, and explains how these rules apply to operations with exponents.
Step-by-step explanation:
In mathematics, we have different rules for operations on numbers that determine the signs of the results. When two positive numbers multiply, as in 2x3, the answer is positive, which is 6. Similarly, when two negative numbers multiply, like (-4) x (-3), the result is also positive, being 12. However, if the two numbers multiplied have opposite signs the answer is negative, examples being (-3) x 2 = -6 and 4 x (-4) = -16.
When a number is divided by another, similar rules for signs apply. For instance, dividing by 8 is the same as multiplying by its reciprocal which is 1/8. Furthermore, division and multiplication rules are used when dealing with exponents. If you have a power raised to another power, like 3².³5, you add the exponents to get 3·. A negative exponent indicates division by the number raised to that power; for example, x± means 1/x.
The process of solving equations involves multiple methods that yield the same result, and it's important to apply multiplication or division to every term on both sides of the equation. For instance, multiplying by 1/8 or dividing all terms by 8 has the same effect. Basic addition, subtraction, and their respective rules of signs, such as changing the sign of a number before adding when subtracting, are fundamental to performing arithmetic operations.