Simplify Exponents Questions with Solutions

Questions on simplifying exponents are presented. The answers to the questions are at the bottom of the page and the solutions with full explanations are also included.

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Rules of Exponents

You may need to review a comprehensive list of exponents rules before you start solving the questions below.

Questions with Solutions


  1. \( 27 \left(\dfrac{1}{9}\right)^2 \left(\dfrac{9^2}{3^5} \right) = \)
    A) 9
    B) 18
    C) 1/18
    D) 27
    E) 1/9


  2. \( 80 \left(\dfrac{1}{5^{-1}}\right)^2 \left(\dfrac{25^{-1}}{4}\right)^2 = \)

    A) 1/5
    B) 5
    C) 25
    D) 1/25
    E) 16


  3. For x and y not equal to zero, the expression
    \( \left(\dfrac{x^4}{y^5}\right)^3 \left(\dfrac{y^2}{x^2}\right)^2 \)
    simplifies to
    A) \( \dfrac{x^6}{y^3} \)
    B) \( \dfrac{x^8}{y^{11}} \)
    C) \( \dfrac{x^{11}}{y^4} \)
    D) \( \dfrac{x^8}{y^3} \)
    E) \( \dfrac{x^6}{y^{11}} \)


  4. For \( x \ne - y \), \( \dfrac{3(2x + 2y)^5}{4 (x + y)^3} = \)
    A) \( \dfrac{3}{4} (x^2 + y^2) \)
    B) \( 24(x+y)^3 \)
    C) \( 24(x+y)^2 \)
    D) \( \dfrac{3}{2} (x+ y)^{\frac{5}{3}} \)
    E) \( 24(x^2 + y^2) \)


  5. For x and y not equal to zero, the expression
    \( \left(\dfrac{x^0}{2y}\right)^2 \left(\dfrac{y^4}{x^3}\right)^2 \)
    simplifies to
    A) \( \dfrac{y^6}{2x^6} \)
    B) \( \dfrac{y^4}{ 4 x^4} \)
    C) \( \dfrac{y^4}{4} \)
    D) \( \dfrac{y^6}{4 x^6} \)
    E) \( \dfrac{1}{4 x^4} \)




  6. \( (- 3 x^2 y^3) (- 4 x^3 y^5) = \)
    A) \( -12 x^5 y^8 \)
    B) \( 12 x^5 y^8 \)
    C) \( 12 x^6 y^{15} \)
    D) \( \dfrac{9}{64} x^5 y^8 \)
    E) \( \dfrac{9}{64} x^6 y^{15} \)


  7. For x and y not equal to zero, the expression
    \( \dfrac{12 x^3 y^{-2}}{4 x^{-2}y^3} \)
    simplifies to
    A) \( \dfrac{3 x^5}{y^5} \)
    B) \( 27648 x^5 y^{5} \)
    C) \( 48 x^5 y \)
    D) \( 3 x y \)
    E) \( x y\)


  8. For x and y not equal to zero,
    \( \left(\dfrac{3 x^{-2}}{y^2}\right)^{-2} = \)
    A) \( 9 x^4 y^4 \)
    B) \( 9 x^{-4} y^{-4} \)
    C) \( \dfrac{x^{-4} y^{-4}}{9} \)
    D) \( \dfrac{x^{-4} y^{4}}{9} \)
    E) \( \dfrac{x^{4} y^{4}}{9} \)


  9. For x and y not equal to zero, the expression
    \( \left( \dfrac{2x^2y^{-1}}{5} \right)^2 \left(\dfrac{5 x^{-1}y^3}{4}\right)^3 \)
    simplifies to
    A) \( 5 x^4 y^7 \)
    B) \( \dfrac{5}{16} x y \)
    C) \( \dfrac{5}{16} x y^7 \)
    D) \( \dfrac{5}{16} x^4 y^7 \)
    E) \( \dfrac{5}{4} x^4 y^7 \)


  10. For x and y not equal to zero,
    \( \left(\dfrac{x^{-1}}{y^0} \right)^2 \left(\dfrac{x^2}{y^3}\right)^3 = \)
    A) \( \dfrac{x}{y} \)
    B) \( \dfrac{x^2}{y^4} \)
    C) \( \dfrac{x^4}{y^6} \)
    D) \( \dfrac{x^4}{y^9} \)
    E) undefined


  11. For \( y \ne 0 \), the expression
    \( \left(\dfrac{x^2}{y^3}\right) \left(\dfrac{8x}{y}\right) \left(\dfrac{x^2}{4}\right)^2 \)
    simplifies to
    A) \( \dfrac{2 x^4}{y^4} \)
    B) \( \dfrac{ x^7}{2 y^4} \)
    C) \( \dfrac{ x^4}{8 y^4} \)
    D) \( \dfrac{ x^4}{y^4} \)
    E) \( \dfrac{ x^4}{16 y^4} \)

Answers to the Above Questions
  1. E
  2. A
  3. B
  4. C
  5. D

  6. B
  7. A
  8. E
  9. C
  10. D
  11. B



More References and Links

Exponents Questions and rules.
Solutions and detailed explanations to the above questions.

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