7 Mid-Chapter Quiz

Do you know HOW?

Simplify each expression.

1. 5 − 1 ( 3 − 2 ) 5 super negative 1 end super , open , 3 super negative 2 end super , close
2. ( r − 5 ) − 4 open , r super negative 5 end super , close super negative 4 end super
3. ( 2 x 5 ) ( 3 x 12 ) open 2 , x to the fifth , close open 3 , x to the twelfth , close
4. m n − 4 p 0 q − 2 fraction m , n super negative 4 end super , over p to the . q super negative 2 end super end fraction
5. a 2 b 0 ( a − 3 ) eh squared , b to the , open , eh super negative 3 end super , close
6. ( 3 2 ) − 1 ( 4 m 2 ) 3 open , 3 squared , close super negative 1 end super . open , 4 , m squared , close cubed
7. ( 2 m 3 ) 0 ( 3 m 6 ) − 1 open , 2 , m cubed , close to the . open , 3 , m to the sixth , close super negative 1 end super
8. ( 3 t 2 ) 3 ( 2 t 0 ) − 3 open , 3 , t squared , close cubed . open , 2 , t to the , close super negative 3 end super

Write each number in scientific notation.

9. 48,030,000,000
10. 0.0042
11. 0.0000312
12. 76 million

Write each number in standard notation.

13. 8.3 × 10 9 8.3 times , 10 to the ninth
14. 6.12 × 10 3 6.12 , times , 10 cubed
15. 1.2 × 10 − 4 1.2 times , 10 super negative 4 end super
16. 4.326 × 10 − 1 4.326 , times , 10 super negative 1 end super

Simplify. Write each answer in scientific notation.

17. 0.5 ( 8 × 10 5 ) 0.5 open 8 times , 10 to the fifth , close
18. ( 4 × 10 7 ) ( 3 × 10 − 1 ) open 4 times , 10 to the seventh , close open 3 times , 10 super negative 1 end super , close
19. ( 6 × 10 5 ) ( 1.2 × 10 8 ) open 6 times , 10 to the fifth , close open 1.2 times , 10 to the eighth , close
20. ( 9 × 10 − 3 ) 2 open . 9 times , 10 super negative 3 end super . close squared

21. Astronomy The radius of Mars is about 3.4 × 10 3 3.4 times , 10 cubed  km.

    1. What is the approximate surface area of Mars? Use the formula for the surface area of a sphere, S . A . = 4 π r 2 . cap s . cap a . equals 4 pi , r squared , .  Write your answer in scientific notation.
    2. Write your answer from part (a) in standard form.
22. Geometry A box has a square bottom with sides of length 3 x 2 3 , x squared  cm. The height of the box is 4 x y 4 x y  cm. What is the volume of the box?
23. Evaluate 1 2 a − 4 b 2 1 half . eh super negative 4 end super . b squared  for a = − 2 eh equals negative 2  and b = 4 . b equals 4 .

Do you UNDERSTAND?

24. Reasoning A population of bacteria triples every week in a laboratory. The number of bacteria is modeled by the expression 900 · 3 x , 900 middle dot , 3 to the x , comma  where x is the number of weeks after a scientist measures the population size. When x = − 2 , x equals negative 2 comma  what does the value of the expression represent?

25. Use the properties of exponents to explain whether each of the following expressions is equal to 64.

    1. 2 5 · 2 2 to the fifth , middle dot 2
    2. 2 2 · 2 3 2 squared , middle dot , 2 cubed
    3. ( 2 2 ) ( 2 2 ) 2 open , 2 squared , close . open , 2 squared , close squared
26. Reasoning Is the number 10 5 10 to the fifth  written in scientific notation? Explain.

27. Writing Is the following statement always, sometimes, or never true? Explain your choice.

    A number raised to a negative exponent is negative.

28. Error Analysis Identify and correct the error in the student's work below.

    

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