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# Algebra 2/Trig Name: Unit 3 Notes Packet Date: Period:
Examples: Radical Form (Rads) Rational Exponent Form (No Rads)
√4 412⁄
√𝑥23
𝑥23⁄
√8𝑥2𝑦𝑧45
815⁄ 𝑥
25⁄ 𝑦
15⁄ 𝑧
45⁄ or 2
35⁄ 𝑥
25⁄ 𝑦
15⁄ 𝑧
45⁄
√7𝑥2𝑦4𝑧6
716⁄ 𝑥
13⁄ 𝑦
23⁄ 𝑧
16⁄
Practice: Express using rational exponents (no rads)
E1. √263
E2. √36𝑥5𝑦6 E3. √𝑥610
E4. 4√2𝑎10𝑏3
Express using radical notation (rads)
E5. 𝑥35⁄ E6. 2
57⁄ 𝑎
37⁄ 𝑦
97⁄ E7. 𝑎
23⁄ 𝑔
14⁄ 𝑒
12⁄ E8. 3
23⁄ 𝑤
23⁄ 𝑚
73⁄
Simplify
E9. √325
E10. √−64𝑟6𝑤153 E11.√225𝑥3𝑦8 E12. √(2𝑥 + 1)3
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Express in simplest radical notation (rads + simplify)
E13. 𝑛74⁄ E14. 𝑥
56⁄ 𝑦
32⁄ 𝑧
73⁄ E15. √81
10 E16. (2𝑥)
23⁄ 𝑦
73⁄
Evaluate (with calculator). Round answers to the nearest hundredth (2 decimal places)
E17. √248638
E18. √953
Evaluate (without calculator). The following order might help without a calculator: 1) eliminate negative exp 2) change to radical form 3) simplify rad 4) simplify exp
E19. √643
E20. 4−1
2 E21. (√16)4 2
E22. – (25−3
2)
Solve the equation (use a calculator to approximate answers). Round answers to the nearest hundredth. The following order might help 1) isolate exponent 2) destroy exponent 3) isolate variable (solve for x) E23. 𝑥5 = 243 E24. 6𝑥3 = −1296 E25. 𝑥6 + 10 = 0 E26. (𝑥 − 4)4 = 81
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7.2 Properties of Rational Exponents (include examples with variables) (I/4)
The properties of exponents can be applied to rational exponents to simplify the expression E1. Use the properties of rational exponents to simplify the expression
a. 51
2 ∗ 51
4 b. (81
2 ∗ 51
3)2 c. (24 ∗ 34)−1
4 d. 7
713
e. (12
13
413
)
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P1. Use the properties of rational exponents to simplify the expression
a. 61
2 ∗ 61
3 b. (271
3 ∗ 61
4)2 c. (43 ∗ 23)−1
3 d. 6
634
e. (18
14
914
)
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E2. Use the properties of radicals to simplify the expression.
a. √43
∗ √163
b. √1624
√24
P2. Use the properties of radicals to simplify the expression.
a. √253
∗ √53
b. √323
√43
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E3. Write the expression in simplest form.
a. √543
b. √3
4
5
P3. Write the expression in simplest form.
a. √644
b. √7
8
4
E4. Perform the indicated operation
a. 7 (61
5) + 2 (61
5) b. √163
− √23
P4. Perform the indicated operation
a. 5(43
4) − 3 (43
4) b. √813
− √33
E5. Simplify the expression. Assume all variables are positive.
a. √125𝑦63
b. (9𝑢2𝑣10)12⁄ c. √
𝑥4
𝑦8
4 d.
6𝑥𝑦12
2𝑥13𝑧−5
P5. Simplify the expression. Assume all variables are positive.
a. √27𝑦93
b. (16𝑔4ℎ2)1
2 c. √𝑥5
𝑦10
5 d.
18𝑟𝑠23
6𝑟14𝑡−3
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E6. Write the expression in simplest form. Assume all variables are positive.
a. √5𝑎5𝑏9𝑐135
b. √𝑥
𝑦73
P6. Write the expression in simplest form. Assume all variables are positive.
a. √12𝑑4𝑒9𝑓144
b. √𝑔2
ℎ7
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E7. Perform the indicated operation. Assume all variables are positive.
a. 5√𝑦 + 6√𝑦 b. 2𝑥𝑦1
3 − 7𝑥𝑦1
3 c. 3√5𝑥53
− 𝑥√40𝑥23
P7. Perform the indicated operation. Assume all variables are positive.
a. 8√𝑥 − 3√𝑥 b. 3gℎ1
4 − 6𝑔ℎ1
4 c. 2√6𝑥54
+ 𝑥√6𝑥4
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Warm-ups
Use the provided spaces to complete any warm-up problem or activity
Date: Date:
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Warm-ups
Use the provided spaces to complete any warm-up problem or activity