91Ó°ÊÓ

In the expression \((-1)^5\), it's important to understand the main components: the base and the exponent.
The base is the number that is repeatedly multiplied. In this case, the base is -1.
The exponent (or power) tells us how many times the base is used as a factor. Here, the exponent is 5, meaning we multiply -1 by itself 5 times.
So, in \((-1)^5\), we're looking at the operation \(-1 \times -1 \times -1 \times -1 \times -1\).
This understanding sets the stage for correctly simplifying the expression.

Let's take a closer look at multiplication, especially when dealing with negative numbers like -1:
Normally, multiplication combines a set of quantities into a larger total, but it works slightly differently when negatives are involved.
When you multiply two negative numbers, the result is positive. For example: \(-1 \times -1 = 1\).
If you multiply a positive and a negative number, the result is negative. For example: \(1 \times -1 = -1\).
Applying these rules sequentially for more than two numbers is crucial. Let's break down \((-1)^5\).
First pair: \(-1 \times -1 = 1\). Now, multiply this result with another -1: \(1 \times -1 = -1\).
Continuing: \(-1 \times -1 = 1\).
Finally, \(1 \times -1 = -1\).
Thus, \((-1)^5 = -1\).

Negative numbers are numbers less than zero, represented with a minus sign (-).
They play a unique role in arithmetic, particularly when used as bases in exponential expressions.
Consider the sign when dealing with an odd number of negative factors:
Each pair of negative numbers results in a positive product. However, if there's an odd number of negatives, the final product is negative.
In \((-1)^5\), five negatives mean: four negatives pair up to give positives, and one negative remains.
This one remaining negative makes the part before the base a negative result.
This insight helps predict the outcome of any expression with a negative base.