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Understanding powers and exponents is crucial to simplifying algebraic expressions effectively. A power is represented as a base number raised to an exponent. The exponent indicates how many times the base number is multiplied by itself. For example, in the expression \( 3^2 \), 3 is the base and 2 is the exponent, meaning \( 3 \times 3 \).
- **Calculating Powers and Exponents:** - An exponent of 1 means the number remains the same (e.g., \( 5^1 = 5 \)). - An exponent of 0 (except when the base is zero) equals 1, like \( 7^0 = 1 \). - For the original exercise given, calculate each term separately to simplify: \( 1^8 = 1 \), \( 0^{10} = 0 \), \( 3^2 = 9 \), \( 4^2 = 16 \), and \( 2^3 = 8 \).
Mastering the concept of powers and exponents makes simplifying expressions much smoother. This ensures each component of an expression is approached logically and methodically.

BODMAS/BIDMAS is a mnemonic that helps remember the order of operations used in mathematics. It stands for Brackets, Orders (i.e., powers and roots), Division, Multiplication, Addition, and Subtraction.
- **Application in Simplification:** - Start with any operations in **Brackets** first. In the given exercise, brackets signify the expression \( (4^2 + 2^3) \). - Then proceed to **Orders** or exponents, as previously calculated.- Always perform **Division** and **Multiplication** before moving on to **Addition** and **Subtraction**.
In our specific exercise, this rule directs us to first tackle what's inside the brackets, \( 16 + 8 \), resulting in 24. Next, apply multiplication with 9 before summing the final terms.

The order of operations is a set of rules that determine the correct sequence in which to solve the different parts of a mathematical expression. This ensures consistency in solving expressions by prioritizing different operations.
- **Why Order Matters:** - Misplacing the order can alter results dramatically. For example, solving the expression from left to right without following order rules might yield incorrect results. - **Following the Correct Sequence:** - First, evaluate expressions within brackets. - Second, solve any power and roots as they follow directly after brackets. - Third, handle multiplication or division from left to right. - Lastly, manage any addition or subtraction.
In the step-by-step solution to the exercise, this approach was evident. Starting from focusing on exponents and proceeding logically through brackets, multiplication, and finally, addition, achieving the correct result of 217.