Math Problem Statement

Develop this question in powerpoint format to cut and paste in presentation. What is the value of (5 to the second power – 10) ÷ 5 × 2 to the third power? Show both concrete and visual representation.

Solution

Here's a step-by-step breakdown of the mathematical expression you provided, formatted for a PowerPoint presentation with both concrete and visual representations.


Slide 1: Introduction to the Problem

Title: What is the value of the expression?
Content:

  • Expression: (5210)5×23\frac{(5^2 - 10)}{5} \times 2^3
  • Let's solve this step by step!

Slide 2: Step 1 - Simplifying the Power Operations

Title: Simplifying Powers
Content:

  • 52=5×5=255^2 = 5 \times 5 = 25
  • 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8

Slide 3: Step 2 - Substituting the Simplified Values

Title: Substituting Values into the Expression
Content:
(5210)5×23=(2510)5×8\frac{(5^2 - 10)}{5} \times 2^3 = \frac{(25 - 10)}{5} \times 8 =155×8= \frac{15}{5} \times 8


Slide 4: Step 3 - Simplifying the Division

Title: Simplifying the Division
Content:

  • 155=3\frac{15}{5} = 3
  • Now the expression is:
    3×8=243 \times 8 = 24

Slide 5: Step 4 - Final Answer

Title: Final Answer
Content:

  • The value of (5210)5×23=24\frac{(5^2 - 10)}{5} \times 2^3 = 24

Slide 6: Visual Representation

Title: Visual Breakdown of the Expression
Content:
Concrete Representation:

  1. Power of 5: 52=255^2 = 25
  2. Power of 2: 23=82^3 = 8
  3. Subtract 10 from 25: 2510=1525 - 10 = 15
  4. Divide by 5: 155=3\frac{15}{5} = 3
  5. Multiply by 8: 3×8=243 \times 8 = 24

Visual:

  • Use number blocks for powers. For example, show 5 blocks of 5, 3 blocks of 2, and a subtraction/division with arrows pointing to the final result.

Slide 7: Conclusion

Title: Conclusion
Content:
The value of the expression (5210)5×23\frac{(5^2 - 10)}{5} \times 2^3 is 24.


PowerPoint Template Tips:

  1. Use Visuals: Show step-by-step animations of the numbers being substituted and simplified.
  2. Color Coding: Color the parts involving powers in one color, and the operations (subtraction, division, multiplication) in another to highlight each process.

Would you like further details on how to format or animate these steps in PowerPoint? Or do you have any specific preferences on how to visualize this?

Related Questions:

  1. How do you handle division and multiplication when both appear in an expression?
  2. What other expressions can be simplified using the same steps?
  3. How would this expression change if the order of operations was different (e.g., adding parentheses)?
  4. How do exponents work when they are fractional or negative?
  5. Can you solve similar expressions with different powers or operations?

Tip: Always follow the order of operations (PEMDAS/BODMAS) when solving complex expressions—this ensures accuracy!

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Arithmetic Operations
Order of Operations (PEMDAS)

Formulas

Exponentiation rules (a^b = a * a * ... b times)
Order of Operations (PEMDAS/BODMAS)

Theorems

Exponentiation properties
Order of operations

Suitable Grade Level

Grades 6-8