Powers: math test in the fourth grade (quatrième ).

The chapter on powers is very important and must be understood completely by the student. The latter must be able to master the properties and calculation methods related to this chapter. He/she must show maximum concentration and avoid unnecessary calculation errors. You must read the statement before starting to save time in solving the exercises. This test is an opportunity for you to practice, but it also allows the teacher to check if the students have understood the chapter.

Supervised homework on powers.

Exercise 1
(6 pts)

Give the result of the following calculations in the form “an ” with n a relative integer :

A=(-6)^{-7}\times  ,(-6)^2\\B=(-3)^7\times  ,(-3)^{-4}\\C=(-8)^2\times  ,(-8)^{-5}\times  ,{-8}^{-1}\\D=9^2\times  ,9^{-1}\times  ,9^{-7}\times  ,9^{-4}\\E=\frac{(-6)^{-6}}{(-6)^{-1}}\\F=((-2)^4)^{-3}

Exercise 2: (4 pts)

Give the sign of the following numbers. Justify.




a =2,5^4
b = (-3)^5
c = (-7,1)^{-4}
d = (-2)^{6}\times  ,(-3)^{3}\times  ,4^{-2}

Exercise 3: (2 pts)

Light travels at about 300,000,000 meters per second (m/s). A year consists of approximately 32,000,000 seconds (s).

  1. a. Express these two quantities in scientific writing.

300 000 000 = …

32 000 000 = …

  1. b.
    Calculate a light year, i.e. the distance that light travels in one year.

Power and speed of light

Exercise 4: (2 pts)

A baby is 0.5m long at birth. Knowing that it keeps growing, at an average speed of 0.000 000 005 meter per second, how tall will it be at 3 years old?

Hint: One year consists of about 32,000,000 seconds.

Exercise 5
(6 pts)

Draw a triangle (in the center of the page) ABC such that :

AB = 9.3 cm; AC = 5.8 cm; and BC = 13.7 cm


– in red its mediators. We will call O their point of intersection.

– in green its heights. We will call H their point of intersection.

– in blue its medians. We will call G their point of intersection.

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