Multiplying Monomials with Radical Indices in Algebra II/Trig Honors

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SUMMARY

This discussion focuses on the multiplication of monomials with radical indices in Algebra II/Trig Honors. The participants clarify that when multiplying expressions like 4√[3]{x^5} and √[3]{16x^2}, the index remains consistent throughout the operation. The final simplified result is 8x²√[3]{2x}. Key concepts include understanding the index of the radical, which determines how many times the base is multiplied to achieve the exponent inside the radical. The discussion emphasizes the importance of correctly applying the properties of exponents and radicals.

PREREQUISITES
  • Understanding of monomials and polynomials
  • Familiarity with radical expressions and their indices
  • Knowledge of exponent rules, particularly multiplication and simplification
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of exponents and radicals in detail
  • Practice simplifying radical expressions with various indices
  • Learn how to apply the laws of exponents in algebraic equations
  • Explore advanced topics such as rational exponents and their applications
USEFUL FOR

Students in Algebra II/Trig Honors, educators teaching algebraic concepts, and anyone looking to improve their skills in manipulating radical expressions and understanding monomial multiplication.

  • #31
Thanks, I think that explanation has to do with another part of the lesson in my notes called "Finding the smallest value and smallest integral value"?
What monomial would give me x*x*x*x then? I know it would have to have an index of four. But what exponent would it have to have?
 
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  • #32
x*x*x*x = x^4

\sqrt[4]{x^4} = x

\sqrt[4]{x^4} = (x^4)^{1/4} = x^{4\cdot 1/4} = x^1 = x
 

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