Simplify. Assume that no variable equals 0. (1-18)

1) n^5 • n^2 = n^7

2) y^7 • y^3 • y^2 = y^12

3) t^9 • t^-8

4) x^-4 • x^-4 • x^4

5) (2f^4)^6

6) (-2b^-2 • c^3)^3

7) (4d^2 • t^5 • v^-4) • (-5dt^-3 • v^-1)

8) 8u(2z)^3

9) [12m^8 • y^6] / [-9my^4]

10) [-6s^5 • x^3] / [18sx^7]

11) [-27x^3(-x^7)] / [16x^4]

12) (2 / 3r^2 • s^3 • z^6)^2

13) -(4w^-3 • z^-5)(8w)^2

14) (m^4 • n^6)^4 • (m^3 • n^2 • p^5)^6

15) (3/2d^2 • f^4) ^4 • (-4/3d^5 • f)^3

16) [(2x^3 • y^2] / [-x^2 • y^5) ^-2]

17) [(3x^-2 • y^3)(5xy^-8)] / [(x^-3) ^4 • y^-2]

18) [-20(m^2 • v)(-v) ^3] / [5(-v) ^2 • (-m^4)]

Express each number in scientific notation. (19-21)

19) 896,000

20) 0.000056

21) 433.7 • 10^8

Evaluate. Express the result in scientific notation. (22-24)

22) (4.8 • 10^2) • (6.9 • 10^4)

23) (3.7 • 10^9) • (8.7 • 10^2)

24) [2.7 •10^6] / [9 • 10^10]

25) Write this number in scientific notation: 4,295,000,000

26) Write the answer in scientific notation: 1.86 • 10^5

27)

A) 8 • 10^-7

B) 4.5 • 10^-7

Simplify. (1-24)

1) √24

2) √60

3) √108

4) √8 ∙ √6

5) √7 ∙ √14

6) 3√12 ∙ 5√6

7) 4√3 ∙ 3√18

8) √27su^3

9) √50p^5

10) √108x^6 ∙ y^4 ∙ z^5

11) √56m^2 ∙ n^4 ∙ o^5

12) √8 / √6

13) √2/10

14) √5/32

15) √3/4 ∙ √4/5

16) √1/7 ∙ √7/11

17) √3k/√8

18) √18/x^3

19) √4y/3y^2

20) √9ab/4ab^4

21) 3 / 5 - √2

22) 8 / 3 + √3

23) 5 / √7 + √3

24) 3√7 / -1 - √27

25) t = [√2(750)/9.8]

Use the information to answer 26 and 27.

To estimate how long a thunderstorm will last, meteorologists can use the formula: t = [√d^3/216], where t is the time in hours and d is the diameter of the storm in miles.

26) A thunderstorm is 8 miles in diameter. Estimate how long the storm will last. Give your answer in simplified form and as a decimal.

27) Will a thunderstorm twice this diameter last twice as long? Explain.