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Free Compass Math Practice Questions on Simplifying
Expressions with Exponents with Solutions and Explanations - Sample 9

Solutions with detailed explanations to compass math test practice questions in sample 9.

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

    Solution

    Use rules of exponents to rewrite given expression as

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

    = 27 (1 * 92) / (92 * 35)

    Simplify

    = 27 / 35 = 1 / 9

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

    Solution

    Use rules of exponents to rewrite given expression as

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

    = 80 (1 / 5 -2 )( 25 -2 / 42 )

    = 80 ( 5 2 ) ( 1 / (25 2 42) )

    Simplify

    = 80 (25 / 1002)

    = 80 * 25 / 10,000 = 8 * 25 / 1000 = 200 / 1000 = 1/5

  3. Simplify the expression

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

    Solution

    Use rules of exponents to rewrite given expression as

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

    = (x12 / y15) (y4 / x4)

    Put terms with same variable together

    = (x12 / x4) (y4 / y15)

    Simplify

    = x8 / y11

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

    Solution

    Factor 2 out in the expression (2x + 2y) and write given expression as

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

    Use exponent rules to write expression as

    = 3 25(x + y)5 / [ 4 (x + y)3 ]

    Simplify

    = 3 * 32 (x + y)5 / [ 4 (x + y)3 ]

    = 24 [ (x + y)5 / (x + y)3 ]

    = 24 (x + y)2

  5. Simplify the expression with exponents given below

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

    Solution

    Use rules of exponents to rewrite given expression as

    ( x0 / (2y) )2 (y4 / x3)2 = (1 / 4 y2) (y8 / x6)

    Simplify

    = (1/4)(y8 / y2)(1 / x6)

    = y6 / (4 x6)


  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

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