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

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) \( \dfrac{ x^4}{16 y^4} \)

1. E
2. A
3. B
4. C
5. D
   
   
6. B
7. A
8. E
9. C
10. D
11. B

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