Question

Which statement accurately reflects the result of the expressions (-4)² and -4²?

A) (-4)² is equal to 16, while -4² is equal to -16.
B) Both (-4)² and -4² yield the same result of 16.
C) (-4)² equals -16, whereas -4² equals 16.
D) (-4)² and -4² are distinct, with (-4)² equal to 16 and -4² equal to -16.

Answer 1

D: (-4)² equals 16 because the product of two negative numbers is positive, while -4² equals -16 as the negative sign is outside of the squaring operation.

Step-by-step explanation:

The correct answer is option D: (-4)² and -4² are distinct, with (-4)² equal to 16 and -4² equal to -16. To understand why, we must consider the order of operations and the rules for multiplication of integers.

When we have (-4)², we are squaring -4, which means multiplying -4 by itself, resulting in a positive number, because the rule is that the product of two negative numbers is positive, so (-4) x (-4) = 16. However, in the expression -4², the negative sign is not included in the squaring operation; thus, we are effectively dealing with -(4²). Since 4² is 16, then -4² is -16.