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When tackling a complex mathematical problem, it's essential to follow the correct order of operations to get accurate results. This is where the BIDMAS rules come into play. BIDMAS stands for Brackets, Indices, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right). These rules help you know which operation to perform first.

- **Brackets**: Always solve the expressions contained within brackets first.
- **Indices**: Calculate any powers or roots next.
- **Division and Multiplication**: Perform these operations as they appear from left to right.
- **Addition and Subtraction**: Finally, handle these operations as they come from left to right.

In our exercise, you first tackle anything in parentheses, followed by any indices. Only after these are resolved do you move on to multiplication, division, addition, and subtraction as they occur sequentially in the expression. Correct application of the BIDMAS rules ensures that no mathematical error is made due to processing the operations in the wrong order.

In mathematics, the modulo operation is an arithmetic operation that finds the remainder of division of one number by another. It is often symbolized by the word 'mod'.

The expression \[a \mod n\]results in the remainder when 'a' is divided by 'n'. For example, if we compute\[1216 \mod 2520\],the result is 1216 because 1216 divided by 2520 gives a quotient of 0 and a remainder of 1216. This is due to the fact that 2520 is larger than 1216, meaning the entire "division" is simply 0 with the remainder being the original number.

The modulo operation can be particularly useful in a variety of applications, such as finding patterns within cycles, as it essentially "wraps around" when values reach a certain point. This is a fundamental concept in fields such as computer science and discrete mathematics, where modulo aids in managing fixed bounds or repeated patterns within algorithms.

Math problem solving involves a series of deliberate steps to arrive at a solution. It's a skill that combines creativity and analytical thinking. To effectively solve math problems like the given exercise, you can rely on some systematic strategies.

When presented with a complex expression, it's beneficial to:

• Break the problem down into more manageable parts by isolating and simplifying sections in line with the BIDMAS rules.
• Calculate intermediate results step-by-step, ensuring that each operation connects logically to the next.
• Use techniques like the modulo operation to simplify calculations, especially when dealing with large numbers or cyclic processes.
• Double-check calculations at each stage to minimize error accumulation.

By approaching math problems methodically, students not only solve the given problem but also gain deeper insights into the underlying mathematical concepts, leading to improved skills and confidence in handling various mathematical scenarios.