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IM 8.7.3 Lesson: Powers of Powers of 10

IM 8.7.3 Lesson: Powers of Powers of 10
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2020-08-11 17:24
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① This GeoGebra example demonstrates the exponent rule for powers of powers of 10, allowing students to explore how (10^a)^b simplifies to 10^(a×b) through interactive input fields. ② The core mathematical concepts include the power-of-a-power rule, integer exponents, scientific notation, and properties of exponents, which are fundamental in middle school algebra. ③ Construction details: The example uses the Textfield command to create multiple input boxes (InputBox1 through InputBox9) and the TableText command to organize results into a table, enabling students to compare outcomes for different exponent pairs and discover the pattern. ④ It is suitable for Grade 8 students (ages 13-14) as a classroom exploration or practice tool, and can also serve teachers for demonstrating exponent rules, bridging concrete numerical examples with abstract algebraic reasoning.

GeoGebra Commands & Parameters

  1. Textfield() → InputBox1
  2. Textfield() → InputBox2
  3. Textfield() → InputBox3
  4. Textfield() → InputBox4
  5. Textfield() → InputBox5
  6. Textfield() → InputBox6
  7. Textfield() → InputBox7
  8. Textfield() → InputBox8
  9. Textfield() → InputBox9
  10. TableText({"\bf expression", "\bf expanded", "\textbf{single power\\\quad of 10}"}, {"\phantom{\\\big(}(10^3)^2", "(10\cdot10\cdot10)(10\cdot10\cdot10)", "10^6"}, {"\phantom{\\\big(}(10^2)^5", "(10\cdot10)(10\cdot10)(10\cdot10)(10\cdot10)(10\cdot10)", "10^\phantom{2}"}, {"\phantom{\\\big(}(10\quad)", "\small(10\cdot10\cdot10)(10\cdot10\cdot10)(10\cdot10\cdot10)(10\cdot10\cdot10)", "10^\phantom{2}"}, {"\phantom{\\\big(}(10^4)^2", "", "10^\phantom{2}"}, {"\phantom{\\\big(}(10^8)^{11}", "", "10^\phantom{2}"}, "|_c ") → text9

AI Drawing Prompt Reference

Create an interactive graph demonstrating the exponent rule for powers of powers of 10, featuring multiple input boxes for users to enter exponent pairs and a table displaying results for different pairs, including the original expression, expanded form, and simplified single power of 10 form, to help understand the pattern (10^a)^b = 10^(a×b).
The prompt above was compiled from the original drawing commands and is for reference only.