Final answer:
The absolute value of a number is always non-negative, representing distance from zero. Negative exponents indicate reciprocals, not negative absolute values. In physics, negative values like velocity or acceleration indicate direction, not negative magnitudes.
Step-by-step explanation:
The question asks whether the absolute value can return a negative number. The answer is no, the absolute value of a number refers to its distance from zero on a number line, which is always a non-negative value. For example, the absolute value of both +3 and -3 is 3. This concept also applies to vectors in physics, where multiplying a vector by a negative scalar will reverse its direction, but its magnitude is described by the absolute value and remains positive.
Considering the negative exponents or powers, such as x-n, these indicate the reciprocal of the base raised to the positive exponent. For example, x-4 = 1/x4, which shows that a negative exponent represents a positive fraction and is not related to the concept of absolute values leading to negative numbers.
In physics, phenomena such as velocity and acceleration can be negative, reflecting the direction of motion or the applied force. A negative velocity means the object is moving in the direction opposite to the chosen positive direction, and a negative acceleration indicates that the object is slowing down if it was initially moving in the positive direction, or speeding up if it was moving in the negative direction.
Lastly, in optical systems, a negative magnification means that the image formed is inverted with respect to the object, but the magnitude of that magnification (the absolute value) represents the size of the image relative to the object and is always positive.