# 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. 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 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 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 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 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) (- 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 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 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 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 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 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