Final answer:
The properties illustrated are the Zero Product Property, Distributive Property of Multiplication over Addition (or Subtraction), and Multiplicative Identity Property. Negative exponents represent division by that number with a positive exponent. Multiplication and division rules for signs determine the sign of the result.
Step-by-step explanation:
The student is asking about the property illustrated by each mathematical statement. The properties demonstrated are:
Zero Product Property: 389.0 = 0 shows that any number multiplied by zero is zero.Distributive Property of Multiplication over Addition (or Subtraction): 9.(-1 × x) = 9.(-x) exhibits how multiplication is distributed over addition or subtraction.Multiplicative Identity Property: 7/9 × 1 = 7/9 indicates that any number multiplied by 1 equals the original number.
Additionally, when dealing with negative exponents, such as in x-n, it implies 1 divided by xn. This is reflected in the statement that 3-4 is equivalent to 1/34.
When addressing multiplication of numbers with the same or different signs, the following rules apply:
Two positive numbers yield a positive product.Two negative numbers also yield a positive product.Numbers with opposite signs yield a negative product.
These rules also apply when dividing numbers.