MathPlotAI Logo MathPlotAI

Rule for Dividing Exponents with the Same Base

Rule for Dividing Exponents with the Same Base
Loading the math board and drawing, please wait…
2016-10-21 00:56
FunctionCoordinate Geometry
This example demonstrates the rule for dividing exponents with the same base. Key mathematical concepts include exponent rules. Using GeoGebra commands such as Text, If, Sequence, etc., it dynamically illustrates the application of the exponent rule. Suitable for middle school and above students to learn exponent operations.

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