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Name Chapter 10 Test Math 152 – Bloom √ 1. Rewrite 8 3 x2 y as an exponential expression. 5 3 2. Rewrite 2m /2 n /2 as a radical expression. 3. Simplify i14 √ 4. Simplify −96 √ 5. Let f (x) = 14 − 3x (a) Find the exact value of f (− 32 ) (b) Find the exact value of f (2) 6. Explain how to find the value of 81−3/4 without using a calculator. 3 7. Rationalize the denominator of the expression √ 2 3−4 √ 8. Simplify 18x3 y 6 . 9. Simplify the following using the rules of exponents. Assume all variables represent positive numbers. √ 3 x /4 y 5 (a) √ 1 x /4 y 7 √ 3 (b) x4 · x3/4 (c) (27a2/3 b12 )1/3 10. Completely simplify the following radical expressions. All answers should be exact. √ √ √ (a) 5 5 + 6 20 − 4 18 √ √ √ (b) ( 6 − 3)( 2 − 3) 11. Completely simplify the following expressions. Be sure to write your answers in the proper form. (a) (6 − 5i)(4 + 2i) 2 + 4i (b) 3 − 5i 12. Solve the following equations. √ (a) 2x − 4 − 5 = 1 √ √ (b) 2x − 1 + x = 2 13. Consider a triangle whose vertices are located at the points (1, 3), (7, 3), and (7, 6), as shown: (7, 6) 3 units b (1, 3) b b 6 units (7, 3) • What is the midpoint of the hypotenuse of the triangle? • Use the distance formula to calculate the length of the hypotenuse. • Use the Pythagorean Theorem to confirm that this is a right triangle.