Understanding and Evaluating Expressions Involving Powers: A Comprehensive Guide

When dealing with mathematical expressions that involve powers, it is important to break down each step systematically. This guide will walk you through the process of evaluating a specific expression step by step, without rushing the calculations, and ensure each operation is properly computed.

Understanding Powers

Powers, also known as exponents, represent repeated multiplication. For example, (3^4) means multiplying 3 by itself four times. This concept is fundamental in many areas of mathematics, from basic arithmetic to more advanced topics like algebra and calculus.

Step-by-Step Evaluation of the Expression 34 43 - 52

Let's evaluate the expression (3^4 4^3 - 5^2) step by step. This process will help you understand each component and the final result, ensuring clarity and accuracy.

Step 1: Calculate 34

The value of (3^4) is calculated as follows:

34 is equivalent to 3 × 3 × 3 × 3. Perform the multiplications step by step:

3 × 3 9 9 × 3 27 27 × 3 81

Therefore, (3^4 81).

Step 2: Calculate 43

The value of (4^3) is calculated as follows:

43 is equivalent to 4 × 4 × 4. Perform the multiplications step by step:

4 × 4 16 16 × 4 64

Therefore, (4^3 64).

Step 3: Calculate 52

The value of (5^2) is calculated as follows:

52 is equivalent to 5 × 5. Perform the multiplication:

5 × 5 25

Therefore, (5^2 25).

Step 4: Combine the Results

Now that we have the individual values, we can combine them according to the expression:

34 43 - 52 81 64 - 25

Addition and subtraction are performed according to the order of operations (PEMDAS/BODMAS) where addition and subtraction are left-to-right associative:

81 64 145

145 - 25 120

Therefore, the value of the expression 34 43 - 52 is 120.

Conclusion

Understanding and evaluating expressions involving powers requires a methodical approach, breaking down the problem into smaller, manageable parts. This ensures accuracy and clarity in the final result, which is crucial for both educational and practical applications in mathematics.

Additional Tips for Evaluating Expressions

Always follow the order of operations: AIMDMAS (Addition, Indeterminate multiplication or division, Multiplication, Division, Addition, Subtraction) for consistent results. Break down complex expressions: Divide the expression into smaller components to make it easier to manage. Double-check your work: Verify each step to avoid errors and ensure the final result is correct.

By following these steps, you can confidently evaluate any expression involving powers, ensuring precision in your mathematical calculations.