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When solving math problems, it's crucial to follow the order of operations. The order of operations is often remembered by the acronym PEMDAS:

• P: Parentheses
• E: Exponents
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

This means you should solve equations inside parentheses first, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right).

For example, in the problem \(-4^2\), you first deal with the exponent before applying the negative sign, ensuring you arrive at the correct solution.

Exponents represent repeated multiplication of the base number. For instance, \(4^2\) means multiplying 4 by itself: \(4 \times 4 = 16\). Exponents are an important part of the order of operations (PEMDAS) and must be calculated before any multiplication, division, addition, or subtraction.

Let's look at how exponents work in our problem: \(-4^2\). Here, we calculate \(4^2\) first, giving us 16. Only after calculating the exponent, we apply the negative sign, leading to -16. Remember, the negative sign outside the exponent comes into play later.

Negative numbers can sometimes be tricky in mathematical calculations. A negative number is any number less than zero, indicated by a minus sign (-). When working with negative numbers, it's essential to understand how they interact with other numbers through operations like addition, subtraction, multiplication, and division.

In our example, \(-4^2\), the negative sign affects the whole expression only after computing the exponent. We first find \(4^2 = 16\), and then apply the negative sign, resulting in -16. Not properly managing the negative sign can lead to incorrect answers.

When encountering expressions with negative numbers, always pay careful attention to the placement and order of operations to ensure accuracy.