Name________________________
Date ________
Algebra 2 HW: Exponent Rules & Rational Exponents
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
I.
REVIEW – complete all of these (1 pt each)
1. 3 x  2  3  12
2. 3 x  2  3  12
______
25
3. 3 x  2  12 x
5.
4.
x
2 7
5
1
x2 7
5
II. PRACTICE – Simplify each expression. Assume all variables are positive (1 pt. each)
1. 51/2  53/2
 24
2.  2
3
4. (4  3)2/3
5. (32/3)5/2
6. ( xy 3 )5
 y4 
7.  7 
y 
8. ( y 4 z 2 )( y 3 z 5 )
9. ( 3 fg 5h 2 ) 4
10.
3x 2
9 y 2
11.



3x 2
9x2
2
1
3.  
2
12.
5
x 5 y 8
x 5 y 6
III. MORE PRACTICE – 2 pts each
 2c 3 
13.   4 
d 
2
5
14.
4
16. (3x y )(5 x y )
3
2
7
1
4
19. 5 5
3
6 x 2 y 2 x 3

y3 9x2
(3xy 4 )( 2 x 6 y 2 ) 1
9x 4 y
17.
20.
2
5
3
2
x x y
y10 z
15.
4 x 3 y 3 x 2

y 2 8 x 1
 53
 2c
 4
18.  d
3
6





2
1
21. n 4  n 3
Rewrite the following as two different expressions using the product rule:
22. x7
23. z9
IV. REACH FOR THE STARS! – 3 pts
Represent the following as an expression of exponents using AT LEAST THREE exponent rules.
24.
 16c 4 
 3 
 d 
Name________________________
Date ________
Algebra 2 HW: Square Roots, “i”, and the
Square Root Method for Solving Quadratics
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
25
I. REVIEW – complete all of these (2 pt each)
1.
3.
1
2
x x
44
3
2
3
5
1
3
x x
2.
4.
3
5
4
4
3
5.
5
II. PRACTICE – 1 point each
Simplify using the product rule. Assume all variables are positive.
4. √72
5. √24𝑎2 𝑏 4 𝑐 6
6. √216𝑥 3 𝑦 5
7. √−144
II. PRACTICE :Solve the following equations – 1 pt each
8. x2 = 2x2 + 4
9. 3x2 + 40 = -x2 - 56
10. (x – 3)2 = -16
11. 11x2 = -5x2 - 1
12.
 x  7
2
 196
______
13. x 2  81
x
x
3
5
II. More PRACTICE: Solve the following equations – 2 pts each
14. -2(x – 1)2 = 36
15. 2(x2 – 1) = -14
16. 5  x  3  12  23
2
17. 2 x 2  1152
 5  32
19. 5  x  3  250
18.
 x  2
20.
1 2
x  12
4
21. 9  2 x 2  39
22.
 x  5
23.
2
2
 16
24. 2  x  2   54
2
2
 x  1
2
 25
25. 5 x 2  33  3
Name________________________
Date ________
Algebra 2 HW: Operations with Square Roots & Complex Numbers
Complete the 5 review questions and then choose 20 POINTS worth of new material.
Mix and match as YOU NEED to feel confident with this material.
______
25
I. REVIEW – complete all of these (1 pt each)
1. 3(y – 3) – (4 – y) = 2(y – 1)
2. Evaluate 52
4. Evaluate x2 when x=-5
5. Multiply (x + 5)2
3. Evaluate -52
II. PRACTICE: Simplify. Rationalize the denominators if need be. – 1 point each
6. 13 2 + 4 18
9.
6
2
12. 3√3 ∙ √12
7. 2 12  3 27
10.
4
5
8. 2 50  32 + 3 2
11.
13. 3√3 ∙ √−12
15. (3 – 2i) + (1 + 4i)
16. (5 + i) – (3 – 5i)
17. 4i(3 - 2i)
18. 2i(4 + i)
√24
√48
14. √−6 ∙ 2√2
III. MORE PRACTICE – 2 pts each
Simplify the expression without a calculator. Rationalize if need be.
19.
2i – (2 + 3i) + (1 – 8i)
20. 2(4i – 3) – (8 + i)
21. (4 – 2i)(2 – 3i)
22.
23. (7 – i)(-3 – 4i)
24.
6
25.
(-3 + 4i)(3 – i)
√3𝑥 8
√12𝑥 6
10𝑖 + 6
26.
𝑖
5𝑖
III. REACH FOR THE STARS! Simplify the following. Rationalize if need be – 3 pts each
27.
29.
√16𝑥 2
√24
𝟑𝒊−𝟐
𝒊−𝟔
28.
30.
√16𝑥 2
√24𝑦
𝟒𝒊−𝟐
𝟐𝒊+𝟑