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When working with mathematical expressions that involve multiple operations, such as exponents, multiplication, division, addition, and subtraction, it's crucial to perform these operations in the correct order to get the correct result. This is where the BIDMAS/BODMAS rule comes into play. It stands for Brackets, Indices (or powers and exponents), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

Applying the BIDMAS/BODMAS rule ensures that calculations are performed in the following order: anything inside brackets first, followed by exponents (also known as 'indices' or 'orders'), and then division and multiplication as they appear from left to right, finishing with addition and subtraction as they appear from left to right. Using this rule prevents common mistakes in arithmetic calculations. For example, in the expression given in the exercise, the exponent is evaluated before the multiplication.

Exponents, also called powers, are a shorthand way to express repeated multiplication of a number by itself. An exponent is written as a small number to the upper right of the base number. For instance, in the expression \(3^{2}\), 3 is the base and 2 is the exponent, indicating that 3 should be multiplied by itself once (because 3 to the power of 1 is just 3). So, \(3^{2} = 3 \times 3 = 9\).

Understanding exponents is critical because they are not just about squaring or cubing numbers. Exponents can be any whole number, fractions, or even negative numbers, and they follow specific rules that describe how to manipulate them in calculations. In the context of the given exercise, the power of 2 means the base, 3, is used as a factor twice in the multiplication.

Arithmetic operations are the building blocks of basic mathematics. These include addition, subtraction, multiplication, and division. When performing complex calculations, it's important to have a strong understanding of each operation and how they interact with each other.

Let's focus on multiplication in the context of the given exercise. Once the exponent is evaluated, multiplication is the next step. Multiplication is just repeated addition, and in our exercise, we are multiplying 4 by the result of the exponent, 9. So we are essentially adding the number 9 together 4 times: \(9 + 9 + 9 + 9 = 36\). The final result of the expression is 36. A solid grasp of these operations and the order in which they should be performed, as dictated by the BIDMAS/BODMAS rule, ensures accuracy in solving mathematical expressions.