Exponents and Fractional Expressions Quiz
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Questions and Answers

What is the simplified value of $x$ when $x = rac{(3^2)}{(2^2)} imes rac{(2^4)}{(3^4)}$?

  • $ rac{3^6}{2^6}$
  • $ rac{27}{16}$
  • $ rac{9}{4}$
  • $ rac{3}{2}$ (correct)
  • How is $x^{-2}$ expressed using the properties of exponents?

  • $ rac{1}{x^2}$ (correct)
  • $ rac{3^{-12}}{2^{-12}}$
  • $(-x)^2$
  • $x^4$
  • Which of the following represents the correct calculation of $x^{-2}$ if $x = rac{3^6}{2^6}$?

  • $ rac{2^{12}}{3^{12}}$ (correct)
  • $ rac{3^{-12}}{2^{-12}}$
  • $ rac{3^{12}}{2^{12}}$
  • $ rac{2^{6}}{3^{6}}$
  • What happens to the base when applying the exponent $x^{-2}$ to $x = rac{3}{2}$?

    <p>It becomes the reciprocal of the base raised to the positive exponent</p> Signup and view all the answers

    Given $x = rac{3^6}{2^6}$, what is the value of $(2/3)^{12}$ in relation to $x^{-2}$?

    <p>$x^{-2}$</p> Signup and view all the answers

    Study Notes

    Problem 63

    • Given the equation x = (3/2)² × (2/3)⁻⁴

    • Find the value of x⁻²

    • Solution:

      • x = (3/2)² × (2/3)⁻⁴
      • Using the rule a⁻ⁿ = 1/aⁿ
        • x = (3/2)² × (3/2)⁴
      • x = (3/2)²⁺⁴ = (3/2)⁶
      • x⁻² = 1/x² = (2/3)¹²

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    Description

    This quiz covers properties of exponents and simplification of fractional expressions, focusing on the calculation of $x$ as well as $x^{-2}$. It explores how to express negative exponents using the quotient of bases and determines the value of expressions relating to given values of $x$. Test your understanding of these concepts with this engaging quiz.

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