Mat 121 -- Test 1 Review

I. Rules of exponents. Given the right or left hand side the rule, give the other side. (5 pts each)

1. a^n/b^n	2. a^mn
3. a^ma^n	4. (a/b)^n
5. a^0	6. a^-n
7. a^m - n

II. Rules of radicals. Matching. The number is to be matched with a letter and must be one of the rules of radicals. (5 pts each)

1.	a.
2.	b.
3.	c.
4.	d.
5.	e.
6.	f.
7.	g. a^m/n
8.	h.

III. Factoring, products and fractions. Matching. The number is to be matched with a letter and must yield one of the rules of factoring, products or fractions. (5 pts each)

1. (a + b)(a - b)	a. (a + b)/c
2. (a + b)^3	b. (a - b)^2
3. a/c + b/c	c. ab + ac
4. (ak)/(bk)	d. a^3 - 3a^2b + 3ab^2 - b^3
5. a^2 - 2ab + b^2	e. a/b
6. (a + b)^2	f. (ad/bc)
7. a^3 - b^3	g. (a/c)(b/d)
8. (a + b)(a^2 - ab + b^2)	h. a^2 - b^2
9. (a/b)/(c/d)	i. a^3 + 3a^2b + 3ab^2 + b^3
10. (ab)/(cd)	j. a^3 + b^3
11. (a - b)^3	k. a^2 + 2ab + b^2
12. a(b + c)	l. (a - b) (a^2 + ab + b^2)

IV. Problems. 5 pts each.

1. Write as a power of x:.

2. Simplify .

3. Expand the product: 5(3x - 7) - 3(3x + 1)

4. Expand the product: (r + 4q)(r - 4q)

5. Expand the product: (r + 4y)²

6. Factor completely: 4xy - 8wxy

7. Factor completely: 9x² - 16.

8. Add: 3/4 + 5/6

9. Add: 3x/y + 4x/y - 3z/y.

10. State whether -3.2 < -4 is true or false.

11. Compute the distance between (1, 4) and (8, 4)

12. What is the midpoint of (1, 4) and (8, 4)

13. Evaluate |-100|.

14. Evaluate exactly .

15. Evaluate 4^-3.

16. Eliminate the negative exponents and simplify: x⁵x^-7.

V. Problems. 10 pts each.

1. Eliminate the negative exponents and simplify:

2. Write [(x²)ⁿx⁵]/xⁿ as a power of x.

3. Factor 2x² + 7x - 4 exactly.

4. Add the fractions:

5. Perform the division (x/y)/(2z/x).

6. Simplify completely:

7. Simplify completely:

8. Factor completely: 27a³ - 8b³

9. Simplify completely

10. Add the fractions 5/12 + 7/15

11. 32 is what percent of 96.

12. Show that the following three points are the vertices of a right triangle. (4, 0), (2, 1), (-1, -5)