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When solving any mathematical expression, it's crucial to follow a set rule known as the order of operations. This rule helps ensure that everyone solves the problem in the same way and arrives at the correct answer. The basic rule to remember is PEMDAS, which stands for:

• P: Parentheses
• E: Exponents
• M/D: Multiplication and Division (from left to right)
• A/S: Addition and Subtraction (from left to right)

Order of operations dictates that you first solve any operations inside parentheses, followed immediately by addressing exponents. After exponents, you handle any multiplication or division, moving left to right, and finally, take care of any addition or subtraction moving from left to right.

Sticking to this order entirely changes how we solve problems, and keeps misunderstandings at bay.

Using parentheses in mathematics is like giving specific instructions on what to solve first. It's like highlighting the part of a problem that is most critical. When you see parentheses in an expression, you should always start your calculations from there.

In the problem \((2 \cdot 3)^{2}\), the part inside the parentheses is \(2 \cdot 3\). Before moving on to deal with any exponents, you need to perform this multiplication which results in 6. That simplifies the expression immediately to \(6^{2}\). This leading step makes any future steps easier and ensures the right parts of the expression are tackled first to avoid unnecessary errors.

A mathematical expression is like a language of numbers and symbols that's used to represent a problem. It might include numbers, operators such as addition or multiplication, and sometimes special symbols like parentheses or variables. Each of these components serves a purpose.

In the expression \((2 \cdot 3)^{2}\), all the elements work together to convey a specific calculation process. Multiplication tells us to combine numbers by repeated addition, and the exponent indicates a repeated multiplication of a number by itself. The parentheses highlight what needs to be tackled first, guiding the sequence of operations.

Understanding the structure of a mathematical expression will help you solve it correctly, as you'll recognize the role each part plays and how they interact to form the whole.