University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2024
Views:

281

Pages:

4
Author:

Caroline Mcfarland

H. Algebra 2 Module 11 Review Name: Date: Hour: 11.1 Radical Expressions and Rational Exponents Write each expression in radical form. Simplify numerical expressions when possible. 1.648 2 ^ 15 = 32 2. (6x) ^ (3/7) (sqrt(6x)) ^ 3 3. (- 8) ^ (4/3) (- 2) ^ 4 = 16 4. sqrt^(1/4) [5r ^ 3) sqrt[9] 5r^ 5 27 ^ (2/3) 3 ^ 2 = 9 6. (100a) ^ (1/2) 10sqrt(9) 10 ^ (n/8) $10 sqrt[9* (x ^ 2) ^ 2 pi boxed X^ 4 9. (7x) ^ (- 1/3) Write each expression by using rational exponents. Simplify numerical expressions when possible 10. (root(2, 4)) ^ 7 = 2 ^ (7/4) 3/23/2 11. (sqrt(5x)) ^ 3 5 X (5x) ^ (5/2) 12. root(51 ^ 4, 5) 51 13. (sqrt(169)) ^ 3 165 ^ (3/2) 13 ^ 3 = 2197 14. (root(2v, 4)) ^ 3 * (24) ^ 3 * 4 15. n * 4/5 (root(n ^ 2, 9)) ^ 2 16. 1/((sqrt(3m)) ^ 2) 3m ^ (- 3/2) root(36 ^ 24, 7) 36 ^ (4/6) = 36 ^ 2 1296 18. 1/((root(5p, 5)) ^ 7) (5p) ^ (2/3) 19. In every atom, electrons orbit the nucleus with a certain characteristic velocity known as the Fermi-Thomas velocity, equal to (x ^ (2/3))/137 * c where Z is the number of protons in the nucleus, and e is the speed of light. in terms of c, what is the characteristic Fermi-Thomas velocity of the electrons in Uranium, for with Z =92? 11.2 Simplifying Radical Expressions Simplify each expression. Assume all variables are positive. 1. - 3sqrt(12r) = - 6sqrt(3r) 4 ^ (3/2) * 4 ^ (3/2) 4 ^ (1/2) = 4 ^ 4 = 256 3 (27 ^ (4/2))/(27 ^ (2/3)) 27 ^ (2/3) = 3 ^ 2 = 9 (4)2 4. a2b2b = 04 5. (27 * 64) ^ (3/n) 2 62 3 ^ 2 * 0.4 ^ 2 9.16 = 144 6. (1/243) ^ (2/8) = 1/3 7. (25x)^ 2 3 5x^ 2 - (5 ^ 3 * x ^ (2/2))/(5 ^ 1 * x ^ (1/2)) 5 ^ 2 * x =(25x 8. (4x) ^ (- 1/2) * (9x) ^ (3/2) 2x2 = 3 2 9.3 3 * root(81x ^ 4 * y ^ 2, 3) 27 3 3-3x sqrt(3x) * y ^ 2 9x * root(3x * y ^ 2, 3) 10. - 5 * root(- 500x ^ 5 * y ^ 3, 3) 100 570 ² -25x44x root(32x ^ 7 * y ^ 12 * z, 4) 21 2xy * root(2x ^ 3 * 2, 3) 12. - sqrt(75a ^ 3 * b ^ 6) - 5ab * root(5a, 3) 13. The frequency, f, in Hz, at which a simple pendulum rocks back and forth is given by f = 1/(2pi) * sqrt(rho/(I')) where g is the strength of the gravitational field at the location of the pendulum, and I is the length of the pendulum. a) Rewrite the formula so that it gives the length of the pendulum in terms of g and f. Then simplify the formula using the fact that field is approximately 32ft / (s ^ 2) (8 * (2pi*f) ^ 2)/((2pi*r) ^ 2) = 9/(2pi * r ^ - 2) F = 1/(2pi) * sqrt(4/2 - 1) 2pi*f = J * 9 / e 2pi*rF )^ 2 e P = 20pi * t ^ 2 l = 32/((2pi*F) ^ 2) 2 * 2/((2pi) ^ 2 * f ^ 2) Q = 0.8 / (f ^ 2) b) Use the equation found in part of the , that frequency of 0.52 Hz. l = 0.81/(F ^ 2) l = 0.81/((52) ^ 2) = l = 3ft