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Dividing Powers with the Same Base

Dividing Powers with the Same Base
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2024-10-16 17:46
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This example demonstrates the rule for dividing powers with the same base. The key mathematical concept is the rule of dividing exponents. Using GeoGebra commands such as Textfield, Shuffle, and If, students can interactively learn and verify the exponent division rule. Suitable for 7-8 grade students for practice and understanding.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle({1, 2}) → ModusList, {1, 2}
  4. Shuffle(Sequence[i, i, 4, 14]) → AStartList, {5, 10, 4, 6, 8, 12, 7, 11, 13, 14, 9}
  5. Shuffle(Sequence[i, i, 4, 14]) → AMidList, {13, 6, 11, 9, 4, 14, 10, 12, 8, 7, 5}
  6. If(questionCount < 4, questionCount, 4) → metaprogression
  7. Shuffle(Sequence[i, i, 1, avalue - 1]) → BStartList, {3, 4, 2, 1}
  8. Shuffle(Sequence[i, i, 1, avalue - 1]) → BMidList, {4, 2, 1, 3}
  9. Shuffle(Sequence[i, i, 2, 10]) → XStartList, {10, 5, 4, 3, 2, 9, 8, 6, 7}
  10. Shuffle(Sequence[i, i, -9, 18] \ {0}) → XGanzzhahlList, {11, -1, 13, 1, 7, -7, 16, 15, -4, 18, 9, -9, 12, -8, 14, 4, 6, 2, -3, 17, -2, -6, 10, 3, -5, 8, 5}
  11. Shuffle(Join[{XDezizahlList, XGanzzhahlList}]) → XMidList, {12, -5, 18, 9, 6, 8, 2, -7, -6, -3, 14, -9, 16, 1, 5, 13, -1, 11, 3, 15, 7, 4, -4, 17, -2, 10, -8}
  12. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  13. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 10, 2, 10, 1, 6, 10, 8, 6, 7, 2, 5, 6, 1, 5, 2, 10, 4, 8, 10, 9, 10, 7, 5, 4, 9, 2, 1, 2, 8, 2, 6, 5, 9, 7, 9, 10, 4, 8, 2, 4, 5, 0, 3, 5, 3, 9, 10, 7, 8, 7, 6, 4, 7, 0, 8, 5, 7, 5, 5, 1, 10, 9, 5, 0, 7, 3, 3, 9, 3, 1, 10, 2, 10, 8, 2, 7, 4, 9, 2, 2, 2, 2, 2, 8, 2, 0, 7, 3, 8, 6, 4, 8, 2, 10, 4, 0, 9, 5, 9}
  14. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  15. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 6, 3, 4, 5, 5, 7, 2, 10, 1, 2, 0, 0, 2, 5, 1, 10, 10, 1, 0, 0, 7, 3, 0, 9, 0, 9, 0, 4, 2, 1, 1, 1, 5, 2, 8, 5, 0, 2, 2, 4, 8, 8, 10, 3, 9, 6, 7, 6, 4, 4, 5, 7, 2, 2, 0, 8, 8, 6, 5, 10, 1, 7, 5, 9, 3, 2, 5, 0, 5, 3, 0, 1, 5, 5, 9, 4, 1, 7, 9, 5, 3, 8, 3, 8, 10, 2, 3, 2, 5, 7, 7, 10, 0, 3, 3, 8, 9, 2, 6}
  16. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  17. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  18. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  19. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  20. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  21. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  22. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  23. Text(Text2, E, false, true, -1, 0) → Text6
  24. Text(Text3, F, false, true, -1, 0) → Text7

AI Drawing Prompt Reference

Create an interactive practice figure about dividing powers with the same base. Add two input boxes so a learner can enter the needed numbers for the exponent division problem, and ensure the displayed content varies with the question index. Generate random integer points to define a rectangular working area: use four corner points chosen from the generated points to draw a rectangle frame. Inside the figure, place text labels at key positions within the rectangle to show the symbols for the expression (the dividend and divisor powers) and another text label for the remaining part of the comparison/result. The final layout should visually connect the text to the rectangle’s positions, forming a consistent exercise panel.
The prompt above was compiled from the original drawing commands and is for reference only.