Math Problem Statement

State each alteration on a separate line to build the following expression: The difference between 4 and 7; The quantity is raised to the 3rd power; The new quantity is added by 2; The sum is divided by 5; The quotient is multiplied by -1.

Solution

The question asks you to state each alteration step by step to build the following expression based on the provided instructions. Here's how the steps would be written mathematically:

  1. The difference between 4 and 7: 474 - 7

  2. The quantity is raised to the 3rd power: (47)3(4 - 7)^3

  3. The new quantity is added by 2: (47)3+2(4 - 7)^3 + 2

  4. The sum is divided by 5: (47)3+25\frac{(4 - 7)^3 + 2}{5}

  5. The quotient is multiplied by -1: 1×(47)3+25-1 \times \frac{(4 - 7)^3 + 2}{5}

This is the final expression based on the steps.

Let me know if you'd like further clarifications or if you have any questions!

Follow-up questions:

  1. What is the value of 474 - 7?
  2. How do you calculate (47)3(4 - 7)^3?
  3. Can you simplify the final expression step by step?
  4. What is the importance of following each step without simplifying early?
  5. How would this change if the difference were between 7 and 4 instead?

Tip:

Always keep track of the sequence of operations and carefully follow the order of operations (PEMDAS) when building complex expressions.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Exponentiation
Order of Operations

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8