Honors Algebra 2: Extra Practice on Integral Exponents with Addition

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Simplify. Express your answer using only positive exponents:

  1. \( \displaystyle \frac{(x + y)^{-2}}{(x + y)^{-1}}\)
    2. Solution

    \( \displaystyle \frac{1}{x + y} \)

  2. \( \displaystyle \frac{a^{-1} - b^{-1}}{a^{-1} + b^{-1}}\)
    3. Solution

    \( \displaystyle \frac{b - a}{b + a} \)

  3. \( \displaystyle (z - w)\left(w^{-1} - z^{-1}\right)\)
    4. Solution

    \( \displaystyle \frac{w^2 - 2wz + z^2}{wz} \)

  4. \( \displaystyle \left(d^{-1} + e^{-1}\right)(d + e)^{-1}\)
    5. Solution

    \( \displaystyle \frac{1}{de} \)

  5. \( \displaystyle \left(x^{-1} + y^{-1}\right)^{-2}\)
    6. Solution

    \( \displaystyle \frac{x^2y^2}{\left(x + y\right)^2} \)

  6. \( \displaystyle \left(x^{-1} + x^{-2}\right)^{-1} \)
    7. Solution

    \( \displaystyle \frac{x^2}{x + 1} \)

  7. \( \displaystyle \left(x^{-1} - x^{-2}\right)(x - 1)^{-1}\)
    8. Solution

    \( \displaystyle \frac{1}{x^2} \)

  8. \( \displaystyle (x + y)^{-2}\left(x^{-2} - y^{-2}\right)^{-1}\)
    9. Solution

    \( \displaystyle \frac{x^2 y^2}{(x+y)^3 (y-x)} \)

  9. \( \displaystyle \left(2^{-2} + 3^{-3}\right)^{-1} \)
    10. Solution

    \( \displaystyle \frac{108}{31} \)

  10. \( \displaystyle \left(2x^{-1} + 3x^{-2}\right)^{-1}\)
    11. Solution

    \( \displaystyle \frac{x^2}{2x + 3} \)