BODMAS (also known as BIDMAS or PEMDAS) is an acronym that stands for Brackets, Order (or Indices), Division, Multiplication, Addition and Subtraction. It is a set of rules that dictate the order in which mathematical operations should be carried out to get the correct answer. These rules are essential because, with them, there can be clarity in the order of calculations, which could result in different answers.

Let us go through each letter of BODMAS in more detail:

B is for Brackets. Brackets should always be solved first when performing any calculations, meaning all contained equations should be solved before moving on. Brackets are used to group numbers and operations together to be treated as a single unit. 

For example, in the expression 2 × (3 + 4), the calculation inside the brackets (3 + 4) should be done first, giving a result of 7. Then, we can multiply 2 by 7, giving a final answer of 14.

Example: Simplify the expression 2 × (3 + 4) - 5
Solution: First, we need to calculate inside the brackets: 3 + 4 = 7. Then, we multiply 2 by 7, giving 14. Finally, we subtract 5 from 14, giving a final answer of 9.

O is for Order (or Indices). Exponents or powers represent the number of times a certain number is multiplied by itself. It is a helpful tool when doing calculations with large numbers. For example, 2³ means 2 × 2 × 2, which is equal to 8. If there are multiple exponents in an expression, they should be calculated from left to right.

Example: Simplify the expression 3² + 4³
Solution: First, we calculate 3², which is 9. Then, we calculate 4³, which is 4 × 4 × 4 = 64. Finally, we add 9 and 64, giving a final answer of 73.

D and M are for Division and Multiplication, respectively. These operations have the same priority and should be carried out from left to right, whichever comes first.

Example: Simplify the expression 10 ÷ 2 × 4
Solution: First, we divide 10 by 2, giving 5. Then, we multiply 5 by 4, giving a final answer of 20.

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