91Ó°ÊÓ

Exponents are a way to express repeated multiplication of the same number by itself. They are also known as powers.
For example, in the expression \( a^n \), \( a \) is called the base and \( n \) is the exponent, indicating that \( a \) is multiplied by itself \( n \) times.
Using exponents can simplify situations where a number is multiplied by itself multiple times.

• Example: \( 2^3 = 2 \times 2 \times 2 = 8 \)
• Here, 2 is multiplied by itself 3 times, which equals 8.

In this exercise, after performing the subtraction to get 0, we raise it to the power of 3. Therefore, \( 0^3 = 0 \), because multiplying zero by itself any number of times always results in zero.
Exponents provide a useful shorthand for simplifying complex expressions and are widely used in mathematics to handle large numbers.

Subtraction is one of the basic arithmetic operations. It involves taking one number away from another.
It is represented by the minus sign \( - \), and the result is called the difference.
Subtraction follows some simple rules:

• To subtract, align the numbers one under the other, and subtract each digit starting from the right.
• The order of subtraction matters; unlike addition, changing the order changes the result.

In the given exercise, we subtract two absolute values:

• The absolute value of \(-1\) is \(1\).
• The absolute value of \(1\) is \(1\).

Thus, \(|-1| - |1| = 1 - 1 = 0\).
This part of the exercise illustrates how subtraction can reduce two identical values to zero, setting the stage for the next operation with exponents.

A number line is a visual representation of numbers on a straight line.
It helps in understanding the positioning and distance of numbers from each other.
Key features of a number line:

• Numbers increase to the right and decrease to the left.
• Zero (0) is the central point between positive and negative numbers.

Using a number line simplifies the understanding of absolute values:

• The absolute value is the distance from zero without considering which direction you're moving.
• This distance is always non-negative.

For the numbers \(-1\) and \(1\), both are exactly one unit away from zero on the number line.
Hence, their absolute values are \(1\), which explains why \(|-1|\) and \(|1|\) both equal \(1\).
This concept is crucial as it often forms the basis for more complex mathematics, including handling operations like subtraction and exponents.