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Mathematics LibreTexts

6.2.2: Homework

  • Page ID
    197601
  • This page is a draft and is under active development. 

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    Reading Questions

    1. What does a negative exponent, such as \(a^{-n}\), signify? How can it be rewritten with a positive exponent?
    2. When factoring out the Greatest Common Factor (GCF) from an algebraic expression where terms have different powers of a common base (e.g., \(x^{1/3}\) and \(x^{-2/3}\)), which power of the common base should you factor out?
    3. If you factor \( (1+x)^{-2/3} \) from \( 3(1+x)^{1/3} \), what is the exponent of \( (1+x) \) in the remaining factor inside the parentheses? Show the subtraction of exponents.
    4. When simplifying an expression like \(\frac{2(18+x)^{1/2} - x(18+x)^{-1/2}}{x+18}\) by first factoring out the GCF from the numerator, what is a common GCF to choose?
    5. Describe an alternative method for simplifying an expression like \(\frac{2(18+x)^{1/2} - x(18+x)^{-1/2}}{x+18}\) that involves treating negative exponents as fractions.
    6. Why is it often preferred in Calculus to leave answers with negative exponents rather than converting them to fractions?
    7. When simplifying expressions that arise from the Quotient Rule in Calculus, such as the one in Example 3, why is it generally advisable not to distribute terms in the final overall denominator?
    8. What is the critical concept to remember when factoring out a GCF from an algebraic expression? (Hint: "factoring is a ______ process")

    Homework

    The textbook homework has not been written at this time.


    This page titled 6.2.2: Homework is shared under a not declared license and was authored, remixed, and/or curated by Roy Simpson.

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