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Exponents: Division Rule with Coefficients Demo

Exponents: Division Rule with Coefficients Demo
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2013-09-10 09:53
Coordinate Geometry
In collections Basic Exponents Rules Exponents Exponents Exponents Algebra: Exponents
This example demonstrates the exponent division rule applied to algebraic expressions with coefficients. It involves core math concepts like exponent rules, fractional representation, and geometric transformations. Constructed using GeoGebra commands and objects such as Text, If, Sequence, Translate, Polygon, FractionText, and Segment, it visually illustrates the rule. Suitable for high school mathematics education to help students understand and apply the exponent division rule.

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. If(color, 255.0, 0.0) → factorColor255
  9. If(color, 153.0, 0.0) → factorColor153
  10. Text("x") → text3
  11. If(expX1 - expX2 ≟ 0.0 ∧ expY1 - expY2 ≟ 0.0, 1.0, 0.0) → zeros
  12. Sequence(Translate[xtop, Vector[(0.0, 0.0), (-(0.75) * i, 0.0)]], i, 0.0, expX1 - 1.0) → ExpandXtop
  13. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, 0.0)]], i, 0.0, expY1 - 1.0) → ExpandYtop
  14. Sequence(Translate[xtop, Vector[(0.0, 0.0), (-(0.75) * i, -(1.2))]], i, 0.0, expX2 - 1.0) → ExpandXbot
  15. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, -(1.2))]], i, 0.0, expY2 - 1.0) → ExpandYbot
  16. Translate((6.923609046978582, -1.782455570499752), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → A
  17. Translate((6.923609046978582, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → B
  18. Translate((7.524258469913336, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → C
  19. Translate((7.524258469913336, -1.782455570499752), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → D
  20. Polygon(A, B, C, D) → ShadeNotePoly, a_1, b_1, c_1, d_1
  21. 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
  22. 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
  23. Text("_________________________") → text7
  24. If(coef1 ≟ 0.0, 1.0, coef1) → coef1b
  25. FractionText(coef1b / coef2) → DivRuleFracText2
  26. FractionText(coef1b / coef2) → DivRuleFracText
  27. Segment(E, F) → a
  28. FractionText(coef1b / coef2) → ExpFormCoefOnlyText
  29. If(coef2 ≟ 0.0, 1.0, coef2) → coef2b
  30. Segment((7.5 - 0.75 * If[expX1 > expX2, expX1, expX2] - If[coef1b > 1.0 ∧ coef1b < 2.0 ∧ coef2b > 1.0 ∧ coef2b < 2.0, 0.0, If[coef1b < -(9.0) ∨ coef2b < -(9.0), 1.2, 0.7]], -(0.5)), (7.5 + 0.75 * If[expY1 > expY2, expY1, expY2], -(0.5))) → ExpandDivLine
  31. If(coef2 ≟ 0.0, Text[coef1b + ""], FractionText[coef1b / coef2b]) → ExpFrmCoefFraction
  32. Text(abs(expX1 - expX2) + "") → ExpandFracXexp
  33. Text(abs(expY1 - expY2) + "") → ExpandFracYexp
  34. FractionText(coef1b / coef2) → text13

AI Drawing Prompt Reference

Create a mathematical illustration demonstrating the exponent division rule with coefficients. Center a rectangle labeled with axes for variables y and x. Above and below the rectangle, use arrows to indicate exponent changes, with the number of arrows corresponding to the exponent values. Inside the rectangle, display the result of dividing coefficients as both a fraction and a decimal. On the left and right sides, include pairs of rectangles connected by arrows to show the process of subtracting exponents. At the bottom, draw a line segment whose length relates to the exponent difference, labeled with the result of dividing coefficients.
The prompt above was compiled from the original drawing commands and is for reference only.