Zero & Positive Exponent Game

Zero & Positive Exponent Game
Welcome to the Power-Up Lab. This game is designed to test your mastery of exponents through a sci-fi “core calibration” interface. Scroll down the page for a detailed explanation.
 

 

How to Play the Zero & Positive Exponent Game
Phase 1: Configuration
Before you begin, you must set the parameters of your “Power Core” on the Main Menu:
Max Base: Sets the highest possible number that will be used as the large bottom number.
Max Exponent: Sets the highest possible power (the small top number).
Standard Mode: Problems will use exponents from 1 up to your chosen maximum.
With 0 Mode: Adds the Zero Rule into the mix, meaning you will see problems with an exponent of 0.

Phase 2: Solving Problems
Once the game starts, you’ll see a large number (the Base) and a smaller number (the Exponent), such as 5³. You must fill in two data points to “Calibrate the Core”:

1. Expanded Form
   This shows the logic behind the power.
   Standard: Type the base multiplied by itself the number of times shown in the exponent. Use * or x for multiplication (e.g., for 5³, type 5x5x5).
   The Identity Rule (x¹): If the exponent is 1, the expanded form is just the base itself (e.g., 5).
   The Zero Rule (x⁰): If the exponent is 0, the expanded form is 1.
   

2. Calculated Value
   This is the final result of the math.For 5³ (5 × 5 × 5), you would enter 125.
   

Phase 3: Feedback & Scoring
After clicking Calibrate Core, the system provides a status report:
Power Optimal: You got both the expansion and the value correct. Your success ratio (Correct/Attempted) will increase.
Grid Failure: One or both of your entries were incorrect. The system will provide a hint or the correct result so you can recalibrate for the next round.
Accuracy Tracking: Check the top-right corner to see your Success Rate. Aim for 100% stability

The Three Golden Rules
In your Power-Up Lab game, we focused on these three scenarios:
Standard Multiplication (x^n): The “n” tells you how many times to write the base.
Example: 2^4 = 2 × 2 × 2 × 2 = 16.
The Identity Rule (x¹): Any number to the power of 1 is just itself. The cloning machine hasn’t actually started yet; you just have the original number.
Example: 100¹ = 100.
The Zero Rule (x⁰): This is the one that feels like a “glitch,” but it’s vital. Any non-zero number to the power of 0 is always 1.
The Logic: Think of it as a pattern. Every time you decrease an exponent, you divide by the base.
2³ = 8
2² = 4 (divided by 2)
2¹ = 2 (divided by 2)
2⁰ = 1 (divided by 2)

The video gives a clear, step-by-step approach to practice long division.

• Show Video

 

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