Free Compass Math Practice Questions
on Simplifying Expressions with Exponents - Answers Included

A set of questions, with answers, on simplifying expressions with exponents similar to the questions in the compass math test are presented. The answers to the questions are at the bottom of the page and the solutions with full explanations to these questions are also included.

  1. 27 (1 / 9)2 ( 92 / 35 ) =

    A) 9
    B) 18
    C) 1/18
    D) 27
    E) 1/9

  2. 80 (1 / 5 -1)2 ( 25 -1 / 4 )2 =

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

  3. Simplify the expression

    (x4 / y5)3 (y2 / x2)2

    A) x6 / y3
    B) x8 / y11
    C) x11 / y4
    D) x8 / y3
    E) x6 / y11

  4. 3 (2x + 2y)5 / [ 4 (x + y)3 ] =

    A) (3/4) (x2 + y2)
    B) 24(x + y)3
    C) 24(x + y)2
    D) (3/2)(x + y)5/3
    E) 24 (x2 + y2)

  5. Simplify the expression with exponents given below

    ( x0 / (2y) )2 (y4 / x3)2

    A) y6 / (2 x6)
    B) y4 / (4 x4)
    C) y4 / 4
    D) y6 / (4 x6)
    E) 1 / (4 x4)

  6. (- 3 x2 y3)(- 4 x3y5) =

    A) - 12 x5 y8
    B) 12 x5 y8
    C) 12 x6 y15
    D) (9 / 64) x5 y8
    E) (9 / 64) x6 y15

  7. Simplify the expression

    (12 x3 y-2) / (4 x-2y3)

    A) 3 x5 / y5
    B) 27648 x5 y5
    C) 48 x5 y
    D) 3 x y
    E) x y

  8. For x and y not equal to zero,

    ( 3 x-2 / y2 )-2 =

    A) 9 x4 y4
    B) 9 x- 4 y- 4
    C) x- 4 y- 4 / 9
    D) x- 4 y4 / 9
    E) x4 y4 / 9

  9. For x and y not equal to zero, the expression

    (2 x2 y-1 / 5)2 (5 x-1y3 / 4)3

    simplifies to

    A) 5 x4 y7
    B) (5 / 16) x y
    C) (5/16) x y7
    D) (5/16) x4 y7
    E) (5 / 4) x4 y7

  10. For x and y not equal to zero,

    (x-1 / y0 )2 (x2 / y)3 =

    A) x / y
    B) x2 / y4
    C) x4 / y6
    D) x4 / y4
    E) undefined

  11. Simplify the expression

    (x2 / y3 ) (8 x / y) (x2 / 4)2

    A) 2 x4 / y4
    B) (1/2) x4 / y4
    C) (1/8) x4 / y4
    D) x4 / y4
    E) (1/16) x4 / y4