Math Problem Statement

-4×6^2÷6-(42+5)

Solution

Let's break this down step by step:

Expression: 4×62÷6(42+5)-4 \times 6^2 \div 6 - (42 + 5)

  1. First, evaluate 626^2: 62=366^2 = 36

  2. Next, multiply by 4-4: 4×36=144-4 \times 36 = -144

  3. Now divide by 6: 144÷6=24-144 \div 6 = -24

  4. Evaluate the expression inside the parentheses: 42+5=4742 + 5 = 47

  5. Finally, subtract 47 from 24-24: 2447=71-24 - 47 = -71

So, the result of the expression is: 71\boxed{-71}

Do you need further details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. What happens if the exponent is changed to 3, i.e., 4×63÷6(42+5)-4 \times 6^3 \div 6 - (42 + 5)?
  2. How would the result change if you add a negative number inside the parentheses, like 4×62÷6(425)-4 \times 6^2 \div 6 - (42 - 5)?
  3. Can you simplify the expression if the division comes first, i.e., 4÷6×62(42+5)-4 \div 6 \times 6^2 - (42 + 5)?
  4. What is the effect of swapping the order of multiplication and division in this expression?
  5. What would happen if the parentheses around 42+542 + 5 were removed?

Tip: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)) to avoid mistakes in simplifying expressions.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Order of Operations
Exponents
Basic Algebra

Formulas

Exponentiation: a^n
Division and Multiplication
Addition and Subtraction

Theorems

Order of Operations (PEMDAS)

Suitable Grade Level

Grades 6-8