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Exponents: Division Rule Demo

Exponents: Division Rule Demo
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2013-09-10 09:51
TrigonometryGeometric Construction
In collections Basic Exponents Rules Exponents Exponents Exponents
This example demonstrates the geometric representation and calculation process of the exponent division rule. It involves core math concepts like exponent operations, fraction simplification, and geometric transformations. Constructed using GeoGebra commands like Text, If, Sequence, Segment, Translate, Polygon, it provides dynamic graphics and textual explanations. Suitable for high school mathematics teaching and learning, helping to understand exponent properties and geometric intuition.

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, 0.0) → factorColor255
  10. If(color, 153.0, 0.0) → 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 ≟ 0.0 ∧ expY1 - expY2 ≟ 0.0, 1.0, 0.0) → 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, 0.0), (-(0.75) * i, 0.0)]], i, 0.0, expX1 - 1.0) → ExpandXtop
  23. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, 0.0)]], i, 0.0, expY1 - 1.0) → ExpandYtop
  24. Sequence(Translate[xtop, Vector[(0.0, 0.0), (-(0.75) * i, -(1.2))]], i, 0.0, expX2 - 1.0) → ExpandXbot
  25. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, -(1.2))]], i, 0.0, expY2 - 1.0) → 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[Vector[(0.0, 0.0), (0.0, -3.0)]]) → A
  28. Translate((6.923609046978582, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → B
  29. Translate((7.524258469913336, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → C
  30. Translate((7.524258469913336, -1.782455570499752), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → 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, 0.0), (-(0.73) * i, 0.0)]], Translate[(6.923609046978582, 0.4), Vector[(0.0, 0.0), (-(0.73) * i, 0.0)]], Translate[(7.524258469913336, 0.4), Vector[(0.0, 0.0), (-(0.73) * i, 0.0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0.0, 0.0), (-(0.73) * i, 0.0)]]], i, 0.0, If[expX1 > expX2, expX2, expX1] - 1.0) → ExpandXPairsSeq
  33. Sequence(Polygon[Translate[(6.923609046978582, -1.782455570499752), Vector[(0.0, 0.0), (0.73 * i, 0.0)]], Translate[(6.923609046978582, 0.4), Vector[(0.0, 0.0), (0.73 * i, 0.0)]], Translate[(7.524258469913336, 0.4), Vector[(0.0, 0.0), (0.73 * i, 0.0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0.0, 0.0), (0.73 * i, 0.0)]]], i, 1.0, If[expY1 > expY2, expY2, expY1]) → ExpandYPairsSeq

AI Drawing Prompt Reference

Create a geometric illustration demonstrating the exponent division rule, showing two exponent expressions and their division in fraction form, along with geometric transformations. Start by drawing the two exponent expressions and labeling their values, then connect them with a fraction bar. Use geometric transformations (translations and scalings) to visualize the result of the exponent division, emphasizing the geometric meaning with polygons and lines.
The prompt above was compiled from the original drawing commands and is for reference only.