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Simplify Expression with Positive Exponents

Simplify Expression with Positive Exponents
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2015-09-11 21:52
FunctionCoordinate Geometry
In collections CCSS Support Algebra I Unit 1
This example demonstrates simplifying algebraic expressions involving negative and zero exponents, converting them to positive exponents. Key math concepts include exponent rules, multiplication of like bases, and the zero exponent property. GeoGebra's LaTeX command is used for displaying mathematical formulas. Suitable for middle school and above students learning exponent rules for advanced math preparation.

GeoGebra Commands & Parameters

  1. LaTeX("\text{Use the exponent rule \textcolor{#000099}{a^m\; • \;a^n = a^{m +n}} to simplify the expression.}") → Pg1B
  2. LaTeX((((((((((("\text{\textcolor{#000099}{x^" * X1P) * " \;•\; x^") * X2P) * " = x^{") * X1P) * " + ") * X2P) * "} = x^{") * X12P) * "}}}")) → Pg1E
  3. LaTeX("\text{Use the exponent rule \textcolor{#000099}{a^0 = 1} to further simplify the expression.}") → Pg1G
  4. LaTeX("\text{Substitute 1 for \textcolor{#000099}{z^0}.}") → Pg1I
  5. LaTeX((((((((((((("\text{\textcolor{#000099}{x^{" * X12P) * "} • \;y^{–") * YP) * "} •\; z^0 = x^{") * X12P) * "} • \;y^{–") * YP) * "} •\; 1 = x^{") * X12P) * "} • \;y^{–") * YP) * "}}}")) → Pg1J
  6. LaTeX("\text{Use the exponent rule \textcolor{#000099}{a^{−m} = \frac{1}{a^m}} to write the negative exponent as a positive exponent.}") → Pg2A
  7. LaTeX("\text{\textcolor{#000099}{a^{−m} = \frac{1}{a^m}}}") → Pg2C
  8. LaTeX((((("\text{\textcolor{#000099}{y^{−" * YP) * "} = \frac{1}{y^") * YP) * "}}}")) → Pg2D
  9. LaTeX((((("\text{Substitute \textcolor{#000099}{\frac{1}{y^" * YP) * "}} for \textcolor{#000099}{ y^{–") * YP) * "}}.}")) → Pg2E
  10. LaTeX((((((((((((("\text{\textcolor{#000099}{x^{" * X12P) * "} •\; y^{−") * YP) * "} = x^{") * X12P) * "} • \frac{1}{y^") * YP) * "} = \frac{x^{") * X12P) * "}}{y^") * YP) * "} }}")) → Pg2F
  11. LaTeX((((((((((("\text{The expression \textcolor{#000099}{x^" * X1P) * " •\; y^–^") * YP) * "\; • \; x^") * X2P) * "•\; z^0} can be simplified to \textcolor{#000099}{\frac{x^{") * X12P) * "}}{y^") * YP) * "}}.}")) → Pg2G
  12. LaTeX((((((((((("\text{The expression \textcolor{#000099}{x^" * X1P) * " \;•\; y^–^") * YP) * "\; • \; x^") * X2P) * "•\; z^0} can now be simplified to \textcolor{#000099}{x^{") * X12P) * "} • \;y^{–") * YP) * "} •\; z^0}.}")) → Pg1F
  13. LaTeX((((("\text{The expression is now simplified to \textcolor{#000099}{x^{" * X12P) * "} •\; y^{–") * YP) * "}}.}")) → Pg1K
  14. LaTeX((("\text{Exponent of y = -" * Linear) * "}")) → DK3
  15. LaTeX((("\text{Exponent of x₁ = " * Quadratic) * "}")) → DK1
  16. LaTeX((("\text{Exponent of x₂ = " * Constant) * "}")) → DK2
  17. LaTeX((((((("\text{Simplify the expression \textcolor{#000099}{x^" * X1P) * "\; •\; y^–^") * YP) * "\; • \; x^") * X2P) * "\;•\; z^0}. Write the expression using only positive exponents.}")) → Pg1A
  18. LaTeX("\text{To multiply powers with the same base, add the exponents.}") → Pg1C
  19. LaTeX((((((((((("\text{In the expression \textcolor{#000099}{x^" * X1P) * " \;•\; y^–^") * YP) * "\; • \; x^") * X2P) * "\;•\; z^0}, the only terms with the same base are \textcolor{#000099}{x^") * X1P) * "} and \textcolor{#000099}{x^") * X2P) * "}. To multiply these terms, add the exponents.}")) → Pg1D
  20. LaTeX("\text{Any value to the 0 power equals 1. Thus, \textcolor{#000099}{z^0 = 1}.}") → Pg1H
  21. LaTeX("\text{To rewrite a negative exponent as a positive one, take its reciprocal.}") → Pg2B
  22. LaTeX("\text{\mathbf{exponent} \text the number of times a factor is being multiplied together in an}") → WTK1
  23. LaTeX("\text{exponential expression; in the expression \textcolor{#000099}{a^b}, \textcolor{#000099}{b} is the exponent}") → Wtk2