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Exponents- Division Rule Demo

Exponents- Division Rule Demo
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2017-11-21 22:29
FunctionCalculusGeometric ConstructionSlider Animation
This example dynamically demonstrates the division rule of exponents, visually showing the process of subtracting exponents when the base is the same. It involves core math concepts like exponent operations, function graph transformations, and analytical geometry. GeoGebra commands and objects such as Text, If, Sequence, Segment, Translate, Polygon are used to create step-by-step visualizations and interactive verifications. Suitable for high school mathematics teaching to help students understand and master exponent rules, enhancing mathematical visualization skills.

GeoGebra Commands & Parameters

  1. Text("y") → text4
  2. Text("y") → text6
  3. Text("x") → text5
  4. Text(expX1 + "") → text8
  5. Text(expX2 + "") → text9
  6. Text(expY1 + "") → text10
  7. Text(expY2 + "") → text11
  8. Text("________________") → origFracLine
  9. If(color, 255, 0) → factorColor255
  10. If(color, 153, 0) → factorColor153
  11. Text("x") → text3
  12. Text("________________") → fracLine
  13. Text(abs(expX1 - expX2) + "") → fracXbotYbotExp
  14. Text(abs(expY1 - expY2) + "") → fracYbotXbotExp
  15. Text(expY1 - expY2 + "") → fracYtopXbotExp
  16. Text(abs(expX1 - expX2) + "") → fracXbotYtopExp
  17. If(expX1 - expX2 ≟ 0 ∧ expY1 - expY2 ≟ 0, 1, 0) → zeros
  18. Text(expX1 - expX2 + "") → fracXtopYtopExp
  19. Text(abs(expY1 - expY2) + "") → fracYbotXtopExp
  20. Text(expX1 - expX2 + "") → fracXtopYbotExp
  21. Text(expY1 - expY2 + "") → fracYtopXtopExp
  22. Sequence(Translate[xtop, Vector[(0, 0), (((-0.75) * i), 0)]], i, 0, expX1 - 1) → ExpandXtop
  23. Sequence(Translate[ytop, Vector[(0, 0), ((0.75 * i), 0)]], i, 0, expY1 - 1) → ExpandYtop
  24. Sequence(Translate[xtop, Vector[(0, 0), (((-0.75) * i), (-1.2))]], i, 0, expX2 - 1) → ExpandXbot
  25. Sequence(Translate[ytop, Vector[(0, 0), ((0.75 * i), (-1.2))]], i, 0, expY2 - 1) → ExpandYbot
  26. Segment((7.5 - (0.75 * If[expX1 > expX2, expX1, expX2]), (-0.5)), (7.5 + (0.75 * If[expY1 > expY2, expY1, expY2]), (-0.5))) → ExpandDivLine
  27. Translate((6.923609046978582, -1.782455570499752), Vector[(0, 0), (0, -3)]) → A
  28. Translate((6.923609046978582, 0.217544429500248), Vector[(0, 0), (0, -3)]) → B
  29. Translate((7.524258469913336, 0.217544429500248), Vector[(0, 0), (0, -3)]) → C
  30. Translate((7.524258469913336, -1.782455570499752), Vector[(0, 0), (0, -3)]) → D
  31. Polygon(A, B, C, D) → ShadeNotePoly, a_1, b_1, c_1, d_1
  32. Sequence(Polygon[Translate[(6.923609046978582, -1.782455570499752), Vector[(0, 0), (((-0.73) * i), 0)]], Translate[(6.923609046978582, 0.4), Vector[(0, 0), (((-0.73) * i), 0)]], Translate[(7.524258469913336, 0.4), Vector[(0, 0), (((-0.73) * i), 0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0, 0), (((-0.73) * i), 0)]]], i, 0, If[expX1 > expX2, expX2, expX1] - 1) → ExpandXPairsSeq
  33. Sequence(Polygon[Translate[(6.923609046978582, -1.782455570499752), Vector[(0, 0), ((0.73 * i), 0)]], Translate[(6.923609046978582, 0.4), Vector[(0, 0), ((0.73 * i), 0)]], Translate[(7.524258469913336, 0.4), Vector[(0, 0), ((0.73 * i), 0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0, 0), ((0.73 * i), 0)]]], i, 1, If[expY1 > expY2, expY2, expY1]) → ExpandYPairsSeq

AI Drawing Prompt Reference

Create a dynamic visualization showing the division rule of exponents, visually demonstrating the process of subtracting exponents when the base is the same. Include function graphs, a slider to control variables, text annotations for exponents and operations, and vector visualizations for exponent changes. Use polygons and segment lines to assist in explaining the process. Start with the basic framework, then dynamically generate visualizations of exponent changes based on slider values, and finally emphasize the result with polygons and segment lines.
The prompt above was compiled from the original drawing commands and is for reference only.