Part 18

4. (x - y^2)/(x^(1/3) - [y^2]^(1/3)).

Multiply:

5. [a^(-3/4) + 2/(m^(1/2))]^2.

6. (K^(-2/7) - g^(-11/25))^2.

7. (r^(2s) + l^(-3m))(r^(2s) - l^(-3m)).

8. [a^(-2) + b^(-3) - 1/(c^2)]^2.

9. (3K^x + 4t^(-3))(3K^x - 7t^(-3)).

10. (2y^(2/7) - 40K^3)(3y^(2/7) + 55K^3).

Factor:

11. x^(2/3) - 64.

12. y^(3/5) + 27.

13. b^(3/2) - 8m^(-1).

14. 3p - 8p^(1/2) - 35.

Factor, using radicals instead of exponents:

15. 60 - 7[3b^(1/2)] - 6b.

16. 15m - 2[^(1/2)] - 24n.

17. a - b (factor as difference of two squares).

18. a - b (factor as difference of two cubes).

19. a - b (factor as difference of two fourth powers).

20. Find the H. C. F. and L. C. M. of x^2 + xy^(1/2) - 2y, 2x^2 + 5xy^(1/2) + 2y, 2x^2 - xy^(1/2) - y.

21. Solve (short method) (x - 7)/(x - 8) - (x - 8)/(x - 9) = (x - 4)/(x - 5) - (x - 5)/(x - 6).

22. Simplify (ab/c + bc/a + ca/b)/(a/bc + b/ca + c/ab) x [((a + b + c)^2)/(ab + bc + ca) - 2]. (Princeton.)

1. Solve for p: 2^(p - 3) = 128.

2. Solve for t: t^(3/2) = -27.

3. Find the square root of 8114.4064. What, then, is the square root of .0081144064? of 811440.64? From any of the above can you determine the square root of .081144064?

4. The H. C. F. of two expressions is a(a - b), and their L. C. M. is a^2b(a + b)(a - b). If one expression is ab(a^2 - b^2), what is the other?

5. Solve (short method): 5/(7 - x) - [(2-1/4)x - 3]/4 - (x + 11)/8 + (11x + 5)/16 = 0.

6. Solve 2/m - 3/n + 10/p = -3, 4/m + 5/p + 6/n = 15, 1/m - 1/n + 5/p = -1/2.