Math Problem Statement

Evaluate the exponential expression: 6 * (4 + 2)^2 - 3^2.

Solution

The problem asks you to evaluate the exponential expression:

6(4+2)2326 \cdot (4 + 2)^2 - 3^2

Let's solve this step by step:

Step 1: Simplify the parentheses

4+2=64 + 2 = 6

So the expression becomes: 662326 \cdot 6^2 - 3^2

Step 2: Calculate the exponents

62=36and32=96^2 = 36 \quad \text{and} \quad 3^2 = 9

Substitute these values into the expression: 63696 \cdot 36 - 9

Step 3: Perform multiplication

636=2166 \cdot 36 = 216

Now the expression is: 2169216 - 9

Step 4: Perform subtraction

2169=207216 - 9 = 207

Final Answer:

The value of the expression is: 207\boxed{207}

Would you like more details on any part of the solution?


Related Questions:

  1. What is the importance of the order of operations in evaluating expressions?
  2. How does squaring a number affect its magnitude compared to the base?
  3. Can this problem be solved using different grouping methods? Why or why not?
  4. What happens if parentheses are missing in similar expressions?
  5. How can we double-check solutions to similar mathematical expressions?

Tip:

Always handle exponents before multiplication and subtraction when solving such problems to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Exponents
Basic Arithmetic

Formulas

Order of Operations (PEMDAS/BODMAS)
Exponentiation rules

Theorems

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Suitable Grade Level

Grades 6-8