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When we talk about squaring numbers, we refer to the process of multiplying a number by itself. It's like saying, 'Please duplicate the number we have!' For example, if we take 3 and square it, we perform the multiplication of 3 by 3, which equals 9. The notation for squaring is simple; you put a little '2' called an exponent, right above the number. So, for 3, it would be written as \(3^2\).

When squaring a fraction, the rule is the same – multiply the top number (the numerator) by itself and do the same for the bottom number (the denominator). Squaring negative numbers might be a bit tricky to remember. The critical thing to realize is that a negative number times itself always gives a positive result because two negatives make a positive. So, squaring \(-\frac{1}{4}\) results in \(\left(-\frac{1}{4}\right)^2 = \frac{1}{16}\), turning the negative fraction into a positive one.

Now, let's talk about the absolute value. Think of absolute value as a distance from zero, no matter in which direction. It's like having a reset button for negative numbers, turning them positive because distance can't be negative, right? You'll recognize the absolute value by its symbol, two vertical lines hugging the number: \(|a|\).

When dealing with the absolute value of a number, remember, you're looking for the 'how far', not 'which direction'. So, if you have a number like \(-5\), its absolute value is simply \(5\) because it's 5 units away from zero on the number line. In our exercise, when you calculate the absolute value of a product that results in \(-\frac{5}{16}\), you ignore the negative, leaving you with a clean, positive \(\frac{5}{16}\).

Finally, let's dive into algebraic addition. When you add numbers together, you are combining their values to find a sum. This process becomes a tiny bit more like a treasure hunt when you're dealing with fractions. You search for a common denominator to put everything on the same playing field. Once your fractions are aligned, with the same base (the denominators), you simply add the top numbers (numerators) together.

Remember, the denominators stay the same; only the numerators take part in the addition. In our case, \(\frac{1}{16} + \frac{5}{16}\), they're already set up for us, sharing a denominator, so we just add the numerators to get \(\frac{6}{16}\). And to make things even simpler, if there’s a chance to reduce our answer to a simpler form by dividing the top and bottom by the same number, we should definitely do it. That's why we get \(\frac{3}{8}\) as the final answer in the exercise.