Math Problem Statement

Which expression is equivalent to (3 - 2^2) + 5?

Solution

The given expression is:

(322)+5(3 - 2^2) + 5

First, simplify the expression inside the parentheses:

22=42^2 = 4

Thus, the expression becomes:

(34)+5=1+5(3 - 4) + 5 = -1 + 5

Now simplify:

1+5=4-1 + 5 = 4

We need to find which expression is equivalent to 4. Let's check the options:

  1. 3253^2 - 5: 32=9,95=43^2 = 9, \quad 9 - 5 = 4 This matches the original expression, so this is the correct option.

Would you like more details or have any further questions?

Here are 5 related questions:

  1. How would the expression change if the exponent were a fraction?
  2. What is the general rule for simplifying expressions with exponents?
  3. How can we simplify expressions that involve negative exponents?
  4. How do parentheses affect the order of operations in mathematical expressions?
  5. Can you give an example where parentheses lead to different results without them?

Tip: Always remember to follow the order of operations (PEMDAS) when simplifying mathematical expressions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification
Order of Operations

Formulas

Exponentiation (a^n)
Order of Operations (PEMDAS)

Theorems

None

Suitable Grade Level

Grades 6-8