91Ó°ÊÓ

In mathematics, an exponent indicates how many times a number, known as the base, is multiplied by itself. When you see an expression like \(-12^{2}\), the exponent is 2. This means you need to multiply \(-12\) by itself.
Here, 2 is used to square the base number.
Squaring a number is one of the most common exponentiation operations, and it's essential to grasp this concept as it appears often in algebra and other higher-level math courses.
Therefore, when you see a base with an exponent, just remember it’s a repeated multiplication of the base by itself.

Now let's delve into what happens when you multiply negative numbers.
When you multiply two negative numbers, the product (result) is always positive. This fact might seem counter-intuitive at first, but understanding the rule can help simplify many math problems.
To multiply two negative numbers, you just multiply the absolute values (numbers without considering their signs) and then apply the rule: as they are both negative, their product is positive.
For example, with the given exercise of \(-12 \times -12\), first multiply the numbers as if they were positive: \(12 \times 12 = 144\). Since both \(-12\) values are negative, applying the rule tells us the product is positive: therefore, \(-12 \times -12 = 144\).

Whenever you multiply or raise negative numbers to an even power, the result, or product, turns out to be positive.
This is because the pairs of negative signs cancel each other out. In our exercise, squaring \(-12\) (multiplying it by itself) results in a positive product because \(- \times - = +\).

Keep this rule of thumb in mind: an even number of negative factors yields a positive product, while an odd number of negative factors yields a negative product.
Understanding this rule will help you solve similar problems much faster and more accurately.