Name:
Date:
Secondary Math I – 5.5 Assignment: Properties of Rational Exponents
Period:
Mr. Heiner
Name of Formula
Formula
Definition of Variables
Volume of a Sphere
4
𝑉 = 𝜋𝑟 3
3
𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠
Period of a Pendulum
𝐿
𝑇 ≈ 2𝜋√
𝑔
𝐿 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑝𝑒𝑛𝑑𝑢𝑙𝑢𝑚
𝑔 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦
Wingspan of a Bird
𝐿 = 2.43𝑤 5000
1663
𝑤 = 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑏𝑖𝑟𝑑
1. Use the formulas in the table to answer the questions.
a. Determine the radius of a sphere with a volume of 904.32 cubic feet. Use 3.14 for π. Show your work.
b. Trevor and Yasmine have rewritten the formula for the period of a pendulum using rational exponents.
Their answers are shown below. Determine which student rewrote the formula correctly, and explain
the mistake the other student made.
1
1
𝐿 −2
𝐿 2
Trevor: 𝑇 ≈ 2𝜋 (𝑔)
Yasmine: 𝑇 ≈ 2𝜋 (𝑔)
c. Rewrite the formula for the length of the wingspan of a bird using radicals and exponents. Explain how
you determined your answer.
8 −3
2. Mr. Ashman writes the expression (27) on the board and asks his students to simplify the expression
completely. The work of three students is shown below. Analyze each students work and determine who
simplified the expression correctly. Explain the mistakes the other students made.
Simplify each expression completely.
Ex. √75𝑥 3 𝑦 = 5𝑥 √3𝑥𝑦
5. 8𝑥 3 ∙ (2𝑥 2 )4
Evaluate each expression.
3
Ex. √216 = 6
3. √81𝑎5
3
4. √256𝑔7 ℎ2
24𝑔2 ℎ−3
(2𝑔)4 ℎ0
7. (2𝑥 3 )2 ∙ 𝑥 4
3
9. √−125
3
12. √−8
7
15. √−1024
16. √5
3
17. √31
19. 6√𝑦
20. √𝑧
6.
8. √64
3
11. √729
4
14. √−128
10. √−343
13. √645
4
3
3
5
Write each radical as a power.
1
4
Ex. √15 = 154
3
18. √𝑥
Write each power as a radical.
1
3
Ex. 123 = √12
1
21. 75
1
1
23. 𝑎2
24. 𝑑5
Write each expression in radical form.
2
3
3
Ex. 53 = √52 = √25
3
28. 𝑥 5
2
26. 85
4
29. 𝑦 3
Write each expression in rational exponent form. Simplify when possible.
3
5
4
31. √84
Ex. √63 = 64
33. √𝑛5
4
34. √𝑝7
4
1
22. 184
1
25. 𝑐 6
3
27. 184
1
30. 𝑐 6
3
32. √122