Math Problem Statement

Solve the expression: (2^7 - (5 - 2)^3 + 3) / (12 - 7 * 2)

Solution

The optical character recognition (OCR) failed to capture the text properly from the image. However, I can manually interpret the equation based on the visible content in the image:

The equation appears to be:

27(52)3+31272\frac{2^7 - (5 - 2)^3 + 3}{12 - 7 \cdot 2}

Let's solve it step by step.

Step 1: Simplify the powers and parentheses

  • 27=1282^7 = 128
  • (52)3=33=27(5 - 2)^3 = 3^3 = 27

So the numerator becomes: 12827+3=104128 - 27 + 3 = 104

Step 2: Simplify the denominator

  • 72=147 \cdot 2 = 14
  • 1214=212 - 14 = -2

Step 3: Final calculation

1042=52\frac{104}{-2} = -52

Thus, the result of the expression is 52-52.

Would you like any further clarification or details? Here are five related questions to explore:

  1. How do you handle powers and parentheses in expressions?
  2. What are the rules for simplifying negative numbers?
  3. How does order of operations (PEMDAS) work in complex equations?
  4. What are common mistakes to avoid when solving fractions with powers?
  5. How can negative results affect the interpretation of an equation?

Tip: Always handle the order of operations carefully, especially when powers and parentheses are involved.

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Math Problem Analysis

Mathematical Concepts

Exponents
Subtraction
Multiplication
Order of Operations
Fractions

Formulas

Exponentiation: a^n
Basic Arithmetic Operations

Theorems

PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

Suitable Grade Level

Grades 7-9