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Solutions with detailed explanations to compass math test practice questions in sample 9.
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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
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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
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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
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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
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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)
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(- 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
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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
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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
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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
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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
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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
Answers to the Above Questions
- E
- A
- B
- C
- D
- B
- A
- E
- C
- D
- B
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