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Math 125 Sample Test 3 1. Simplify. Use positive exponents. 1 (a) a 6 3 a4 1 (b) a 3 b−4 1 a 2 b−3 √ −12 3 (c) a−4 b3 2 (d) 8− 3 (e) a−9 b6 − 2 3 2. Simplify. Assume that each variable can represent any real number. √ (a) 16x2 y 4 √ (b) x2 + 6x + 9 √ (c) 3 8y 3 z 6 √ (d) 4 16x4 y 16 3. Simplify. Assume variables represent nonnegative numbers. √ 3 (a) −8a4 b11 c √ √ 4 4 (b) 4x5 12x2 √ √ √ (c) 4 − 75 + 5 − 2 √ √ √ √ (d) 8 − 6 + 2 + 12 4. Multiply. √ (a) ( 2 + x)2 √ √ √ √ (b) ( 2 − 2 3)( 2 + 2 3) 5. Write the expression using a single radical notation in simplest form. q√ 4 3 4x2 √ √ 6 8 (b) 2 3 (a) 6. Simplify. Write complex expressions in a + bi form. (a) (−3 + 4i)(5 − 2i) 2 − 3i (b) 1 + 2i (c) i142 (d) i−21 7. Rationalize denominator. 1 2xy 8x2 yz 4 √ 1+ 2 √ (b) 3− 2 (a) √ 5 8. Solve. 3 (a) (2 − 3x)− 2 = 27 √ √ (b) 2x − 1 − 4x + 5 = −2 9. Solve the equation by completing the square. 2x2 − 6x + 3 = 0 10. (a) Find the distance between (−2, −4) and (3, −1). (b) Find the midpoint of (−2, −4) and (3, −1). 2