Grade 8 / Powers 86 exercises (100% corrected)

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251053122×53234153×4815×3125 decadizaine101hectocentaines102kilomillier103megamillion106gigamilliard109tera1012 ChingQuizz : 10 exercises available for Quizz assessment : 1. Introduction to powers E.2001 Definition: for a any number and n a strictly positive integer, we call ˇ power of the number a at exponent n ı. This number is noted a n . That is : a n = a × a × · · · × a  n fois Example: 5 3 = 5 × 5 × 5 = 125 ; 7 11 = 7 × 7 × · · · × 7  11 fois = 1977326743 We say: 5 3 is the power of the number 5 at exponent 3 ; 7 11 is the power of the number 7 to the exponent 11 . 1 Using the calculator, give the value of the following prod-ucts : a 3 4 b 2 5 c 7 2 2 Give the mathematical writing of the following numbers : a The power of the number 5 to the exponent 4 ; b The power of the number 4 to the exponent 9 . E.8852 Give the value of each of the follow-ing numbers : a 4 2 b 5 3 c 2 5 d 3 5 e 10 3 E.8853 Associate each of the expressions in power form (left column) with its value (right column) : E.8857 Give the value, in simplified form, of the following powers : a ( − 2) 3 b ( − 2) 4 c 5 2 2 d − 2 3 3 e ( − 1) 100 2. Conducting calculations E.8887 Perform the following calculations : a 5 − 2 × 6 2 b 2 × (30 − 5 2 ) c 4 + 18 − 12 2 E.8888 Perform the following calculations : a 5 2 × 7 2 − 50 b 5 − 5 × 2 − 4 2 2 c 2 − 3 2 − 2 2 − 3 2 E.8889 Perform the following calculations and give the result as an irreducible fraction : a 5 2 − 7 2 5 − 7 2 b 2 − 2 2 × 3 5 2 × 3 − 4 c 5 2 − 3 2 × 2 7 2 3. First use of powers of 10 E.8854 1 Give the values of each of these expressions written as a power of 10 : a 10 3 b 10 6 c 10 9 d 10 11 2 Complete the following blanks with the corresponding positive integers : a thousand is written 1 000 or 10 . . . a million is written 1 000 000 or 10 . . . one billion is written 1 000 000 000 or 10 . . . Note: https://chingmath.fr chapExoCorrec/2001 sacados/2001 chapExoCorrec/8852 sacados/8852 chapExoCorrec/8853 sacados/8853 251053122×53234153×4815×3125 chapExoCorrec/8857 sacados/8857 chapExoCorrec/8887 sacados/8887 chapExoCorrec/8888 sacados/8888 chapExoCorrec/8889 sacados/8889 chapExoCorrec/8854 sacados/8854 decadizaine101hectocentaines102kilomillier103megamillion106gigamilliard109tera1012
E.8855 Complete the blanks with positive integers : 1 The speed of light in a vacuum is about 300 000 000 m = s . This speed can be written : 300 000 000 m = s = 3 × 10 . . . m = s 2 The cities of San Francisco and Wilmington are approxi-mately 400 000 000 cm apart. This distance can be writ-ten : 400 000 000 cm = 4 × 10 ... cm 3 The distance between Earth and Mars is approximately 55.7 million kilometers. This distance can be written : 55 700 000 km = 5.57 × 10 . . . km 4 A duration of 13 years is equivalent to approximately 410 million seconds. This duration can be expressed as : 410 000 000 s = 4.1 × 10 ... s E.8884 1 a How many seconds are contained in an hour? b How many seconds are contained in a day? 2 The speed of light is 300 000 km = s . Indication : the results of the following questions will be indicated in scientific writing a How many kilometers does light travel in one day? b Convert this length into meters. E.2136 In this exercise, any begin-ning of explanation, of approach will be taken into account. Here are the distances (in km) that separate the sun from three planets in the solar system : Venus : 105 × 10 6 ; March : 2 250 × 10 5 ; Earth : 1.5 × 10 8 Which of these three planets is furthest from the sun? Justify. 4. Introduction to algebraic properties E.8856 Looking at the equality below, an-swer the following questions : 3 4 × 3 2 = 3 × 3 × 3 × 3 × 3 × 3 = 3 6 1 Prove equality: 5 4 × 5 2 = 5 6 . 2 Perform the simpifications of the following expressions : C = 7 2 × 7 5 ; D = 5 3 × 5 3 ; E = 3 4 × 3 7 E.8860 1 By simplifying the quotient, justify the equality: 7 8 7 3 = 7 5 . 2 Simplify the following fractions : F = 2 5 2 2 ; G = 7 8 7 11 ; H = 5 2 × 5 10 5 9 E.8861 1 Justify the following equality: I = 2 3 4 = 2 12 2 Expand the following expressions : J = 3 2 ) 5 ; K = (5 4 ) 3 ; L = (7 3 ) 3 E.8862 Proposition: for a a positive integer, m and n two strictly positive integers : a n × a m = a n + m ; a n a m = a n − m ; a n m = a n × m a 5 4 × 5 7 b 6 8 6 5 c 2 5 3 5. Multiplication and power of 10 (positive exponents) E.11268 Proposal: To multiply two powers of the same number, add the exponents. Example: 10 2 × 10 3 = 10 × 10 × 10 × 10 × 10 = 10 5 Simplify the expression of the products : a 10 4 × 10 3 b 10 5 × 10 11 c 10 × 10 6 E.4778 Simplify the writing of the following expressions : a 10 5 × 10 8 b 10 2 × 10 7 c 10 14 × 10 21 E.4779 Simplify the writing of the following expressions : a 10 3 × 10 12 × 10 4 b 2 × 10 5 × 5 × 10 3 E.8858 Simplify the writing of the following expressions : a 10 2 3 b 10 4 2 c 10 3 3 d 10 4 6 6. Division and power of 10 (positive exponents) https://chingmath.fr chapExoCorrec/8855 sacados/8855 chapExoCorrec/8884 sacados/8884 chapExoCorrec/2136 sacados/2136 chapExoCorrec/8856 sacados/8856 chapExoCorrec/8860 sacados/8860 chapExoCorrec/8861 sacados/8861 chapExoCorrec/8862 sacados/8862 chapExoCorrec/11268 sacados/11268 chapExoCorrec/4778 sacados/4778 chapExoCorrec/4779 sacados/4779 chapExoCorrec/8858 sacados/8858
E.11269 Proposal: To divide two powers of the same number, add the exponents. Example: 10 5 10 3 = 10 × 10 × 10 \× 10 × 10 10 × 10 × 10 = 10 × 10 × 10 × 10 × 10 10 × 10 × 10 = 10 2 Simplify the expression of the quotients : a 10 7 10 3 b 10 12 10 7 c 10 4 10 4 E.8859 Simplify the writing of the following expressions : a 10 5 10 2 b 10 12 10 6 c 10 7 10 4 d 10 21 10 14 E.8864 1 Justify the simplification : 5 7 5 9 = 1 5 2 2 Simplify the following expressions : a 12 5 12 10 b 5 4 5 8 c 3 102 3 150 7. Multiplication and division (positive exponents) E.11267 Proposition: for a a positive integer, m and n two strictly positive integers : a n × a m = a n + m ; a n a m = a n − m ; a n m = a n × m a 5 4 × 5 7 b 6 8 6 5 c 2 5 3 E.5653 Simplify the following expressions : A 3 5 × 3 8 b 7 10 7 6 c 6 8 × 6 4 f 6 7 6 4 E.1147 Simplify the following operations : a 7 5 × 7 9 b 5 2 × 5 13 d 6 8 6 7 e 12 8 12 4 E.4780 Simplify the writing of the following powers : b 7 5 × 7 9 c 12 13 × 12 5 d 5 8 5 3 e 13 15 13 7 E.4777 Simplify the writing of the following expressions : a 3 2 × 3 4 b 5 8 × 5 7 c 3 × 3 4 d 3 5 3 2 e 8 3 8 2 f 7 12 7 5 E.8867 Simplify the following expressions : a 3 × 3 5 b 7 4 7 4 c 7 4 × 7 5 × 7 9 E.8866 Simplify the following expressions : a 4 5 4 6 b 3 5 3 8 c 5 3 2 d 3 2 ) 7 8. A little further on E.8863 1 Justify the following equality: I = (2 × 3) 4 = 2 4 × 3 4 2 Expand the following expressions : J = (3 × 5) 3 ; K = (2 × 7) 5 ; L = (2 × 5) 4 E.8865 Simplification of expressions : a 3 5 × 2 5 b 3 2 × 5 2 c 4 3 × 5 3 9. Decimal writing and power of 10 (positive exponent) E.4821 Write the following numbers as dec-imals: a 524.1 × 10 2 b 941.254 × 10 2 c 0.045 × 10 5 E.8870 Arrange the numbers below in as-cending order : A =7.52 × 10 8 ; B =7.47 × 10 9 ; C =7.407 × 10 9 E.4820 For each question, compare the two proposed numbers : a 5.46 × 10 5 et 4.1 × 10 5 b 4.705 × 10 12 et 4.75 × 10 12 c 7.15 × 10 8 et 7.15 × 10 10 d 217 × 10 11 et 2.2 × 10 13 10. Introduction to scientific notation (positive exponent) https://chingmath.fr chapExoCorrec/11269 sacados/11269 chapExoCorrec/8859 sacados/8859 chapExoCorrec/8864 sacados/8864 chapExoCorrec/11267 sacados/11267 chapExoCorrec/5653 sacados/5653 chapExoCorrec/1147 sacados/1147 chapExoCorrec/4780 sacados/4780 chapExoCorrec/4777 sacados/4777 chapExoCorrec/8867 sacados/8867 chapExoCorrec/8866 sacados/8866 chapExoCorrec/8863 sacados/8863 chapExoCorrec/8865 sacados/8865 chapExoCorrec/4821 sacados/4821 chapExoCorrec/8870 sacados/8870 chapExoCorrec/4820 sacados/4820
pico(p)10−12nano(n)milliardième10−9micro(—)millionnième10−6milli(m)millième10−3centi(c)centième10−2deci(ddixième10−1 E.2053 In each case, find the missing num-ber in your head : a 3 × 20 = 15 × x b 8 × 5 = x × 20 c 36 × 4 = 3 × x d 24 × 3 = 8 × x e 22 × 5 = x × 55 f 49 × 2 = 7 × x E.4803 For each question, determine the value of the integer n achieving the equality: a 0.004 5 × 10 n = 4.5 b 0.070 4 × 10 n = 7.04 c 0.000 000 2 × 10 n = 2 E.7996 Write each of the numbers below in the form a × 10 6 where a is a decimal number: a 2.3 × 10 7 b 547.1 × 10 4 c 91 × 10 2 d 0.015 × 10 10 E.5061 Of the following equalities, name the ones that are correct: a 4.42 × 10 15 = 0.442 × 10 14 b 5471 × 10 7 = 5.471 × 10 4 c 0.158 × 10 6 = 15.8 × 10 4 E.3499 Correctly complete the blanks in the following equations : a 354 × 10 54 = 0.354 × 10 ... b 0.000 5 × 10 12 = 50 × 10 ... 11. Power of negative exponent E.8876 Using a calculator, write the follow-ing numbers as decimals : a 2 − 2 b 10 − 3 c 5 − 2 d 0.01 − 1 E.632 Write in decimal form : a 5.4 × 10 − 2 b 6.4 × 10 3 c 7.1 × 10 − 3 E.8874 Definition: For any number a non-zero ( a =0 ) and for any positive integer n , we note : 1 a n = a − n a 0 = 1 ; a 1 = a Examples: 5 3 5 7 = 1 5 4 = 5 − 4 ; 7 − 2 × 7 6 = 1 7 2 × 7 6 = 7 6 7 2 = 7 6 − 2 = 7 4 1 Simplify writing the following quotients in the form a n where n is a positive or negative integer. a 5 6 5 9 b 11 3 11 9 2 Simplify writing the following quotients in the form a n where n is a positive or negative integer. a 4 − 3 × 4 12 b 8 5 × 8 − 10 E.8875 Proposition: Let a be any number and n and m be any two integers. We have the following algebraic properties : a m × a n = a m + n ; a m a n = a m − n ; a m n = a m × n Simplify the following expressions : a 5 − 5 × 5 8 b 7 4 7 10 c 9 − 2 4 12. First use of powers of 10 of negative exponents E.8894 1 Give the values of each of these expressions written as a power of 10 : a 10 − 3 b 10 − 6 c 10 − 9 d 10 − 11 2 Complete the following dotted lines with the correspond-ing positive integers : one thousandth is written as 0 ; 001 or 10 . . . ; one millionth is written as 0 ; 000 001 or 10 . . . ; one billionth is written as 0 ; 000 000 001 or 10 . . . . Note: https://chingmath.fr chapExoCorrec/2053 sacados/2053 chapExoCorrec/4803 sacados/4803 chapExoCorrec/7996 sacados/7996 chapExoCorrec/5061 sacados/5061 chapExoCorrec/3499 sacados/3499 chapExoCorrec/8876 sacados/8876 chapExoCorrec/632 sacados/632 chapExoCorrec/8874 sacados/8874 chapExoCorrec/8875 sacados/8875 chapExoCorrec/8894 sacados/8894 pico(p)10−12nano(n)milliardième10−9micro(—)millionnième10−6milli(m)millième10−3centi(c)centième10−2deci(ddixième10−1
Epaisseurd’uncheveu31pmDiamètred’unatomed’Hélium1mmTailled’unmoustique0;1—mTailled’unecellulehumaine2nmDiamètredel’ADNhumain75—m 104106107101010410510110510−110−210−310−4 E.8895 Relate each object to its average measurement : E.8949 On an ethernet cable, the speed of electricity travels at a rate of 5.6 ns = m . Knowing that the distance between San Francisco and New York is 4100 km , determine the travel time for a signal trav-eling from San Francisco to New York. E.8896 A hair grows about 3 nm every sec-ond. How long does a hair grow in a day? In a year? E.8897 Computer chips are composed of transistors. In 2017, the average size of a transistor was 5 nm (we will assume they are square shaped) . How many transis-tors can a square chip of dimension 5 mm contain at most. 13. Powers of 10 of negative exponents E.7995 1 Using the calculator, connect the numbers with the same value : 2 What conjecture can be made? E.5654 Simplify the following expressions : a 10 5 × 10 − 7 b 10 − 2 × 10 − 2 c 10 − 3 × 10 5 d 10 5 10 7 E.5058 a 10 5 10 − 5 b 10 − 7 10 − 7 c 10 4 × 10 − 2 d 10 3 10 − 3 E.4807 Simplify the writing of the following expressions : a 10 5 10 9 b 10 12 10 9 c 10 25 10 22 d 10 12 10 17 e 10 5 10 − 3 f 10 − 5 10 7 g 10 − 2 10 5 h 10 3 10 − 3 E.2033 Perform the following calculations : A 10 5 × 10 − 8 × 10 − 15 × 10 2 b 10 2 × 10 − 1 × 10 − 2 E.2051 Perform the following calculations : a 10 3 × 10 − 3 10 5 b 10 − 5 × 10 4 10 5 c 10 2 × 10 − 9 10 5 E.2059 Perform the following calculations : a 10 × 10 − 4 10 − 8 b 10 5 × 10 − 4 10 − 3 c 10 − 12 × 10 8 10 4 E.4782 Simplify the writing of the following expressions : a 10 5 × 10 2 10 9 b 10 5 × 10 − 3 c 10 5 10 8 × 10 3 d 10 × 10 5 10 − 2 e 10 2 × 10 − 9 10 − 4 E.8951 a 10 3 10 − 2 4 b 10 16 10 2 8 c 10 5 10 7 2 d 10 3 − 2 E.8877 Perform the following calculations : a 10 3 − 2 b 10 2 10 5 4 c 10 5 × 10 − 6 2 × 10 4 E.8950 a 10 2 × 10 − 4 2 × 10 − 4 b 10 − 3 × 10 5 × 10 − 3 2 14. Product and power division E.8878 Simplify as much as possible the writing of the following expressions. The result will be given as a power: a 6 2 × 6 3 b 5 3 × 5 2 × 5 − 5 c 3 − 4 × 3 5 d 3 2 3 5 e 5 − 4 5 2 f 6 3 6 3 g 6 0 h 5 2 × 3 2 i 1.2 3 × 5 3 E.8879 Simplify the writing of the following powers : a 5 2 × 5 5 b 7 4 × 7 − 7 c 5 × 5 − 4 d 3 5 × 9 e 8 5 × 8 − 3 × 8 − 2 f 5 20 × 5 − 9 https://chingmath.fr chapExoCorrec/8895 sacados/8895 Epaisseurd’uncheveu31pmDiamètred’unatomed’Hélium1mmTailled’unmoustique0;1—mTailled’unecellulehumaine2nmDiamètredel’ADNhumain75—m chapExoCorrec/8949 sacados/8949 chapExoCorrec/8896 sacados/8896 chapExoCorrec/8897 sacados/8897 chapExoCorrec/7995 sacados/7995 104106107101010410510110510−110−210−310−4 chapExoCorrec/5654 sacados/5654 chapExoCorrec/5058 sacados/5058 chapExoCorrec/4807 sacados/4807 chapExoCorrec/2033 sacados/2033 chapExoCorrec/2051 sacados/2051 chapExoCorrec/2059 sacados/2059 chapExoCorrec/4782 sacados/4782 chapExoCorrec/8951 sacados/8951 chapExoCorrec/8877 sacados/8877 chapExoCorrec/8950 sacados/8950 chapExoCorrec/8878 sacados/8878 chapExoCorrec/8879 sacados/8879
15. Decimal writing and power of 10 E.8868 Write the following numbers as dec-imals: a 596.4 × 10 − 1 b 3.3 × 10 − 2 c 7.45 × 10 − 4 E.8869 For each question, compare the two proposed numbers : a 1.7 × 10 − 5 et 1.27 × 10 − 5 b 2.41 × 10 − 5 et 2.41 × 10 − 9 E.8871 Correctly complete the blanks in the following equations : a 654 × 10 − 15 = 6.54 × 10 ... b 0.045 × 10 − 34 = 4.5 × 10 ... E.8872 Of the following equalities, say which are true : a 32 × 10 − 7 = 3200 × 10 − 9 b 5471 × 10 7 = 5.471 × 10 4 c 0.00747 × 10 12 = 747 × 10 17 E.8873 For each question, determine the value of the integer n achieving the equality: a 0.004 5 × 10 n = 4.5 b 0.070 4 × 10 n = 7.04 c 0.000 000 2 × 10 n = 2 16. Scientific notation E.8885 In each case, determine the value of n or x missing verifying equality: a 532 × 10 n = 5.32 b 67 × 10 n = 0.00067 c x × 10 3 = 531.8 d 6.54 × 10 5 = 654 × 10 n e 6.12 × 10 − 13 = x × 10 − 12 f 0.561 × 10 − 7 = 56.1 × 10 n E.4802 1 In each case, determine the value of the integer n verify-ing the equality: a 6794 = 6.794 × 10 n b 0.00354 = 3.54 × 10 n c 3124.1 = 3.1241 × 10 n d 0.0549 = 5.49 × 10 n 2 Use the previous question to determine the scientific no-tation for the following numbers : a 6794 × 10 − 5 b 0.00354 × 10 5 c 3124.1 × 10 5 d 0.0549 × 10 − 3 E.8952 Give the scientific notation for the following numbers : a 0.00176 b 31 970 000 c 0.000 002 127 E.2036 Give the scientific notation of the following numbers : a 531 b 94.14 c 3 526 d 0.000 000 033 2 E.8880 Give the scientific notation for the following numbers : a 3 512 × 10 5 b 0.00173 × 10 − 6 c 0.004 5 × 10 42 E.1152 Write the scientific form of the fol-lowing numbers : a 0.004 5 × 10 6 b 251.37 × 10 − 11 c 0.031 × 10 − 7 E.649 Write the following numbers in scien-tific notation : a 312 × 10 5 b 0.00219 × 10 6 c 3 542 × 10 11 E.3498 Give the scientifc notations of the following numbers : a 546.2 × 10 − 57 b 0.004 5 × 10 − 34 c 39.78 × 10 15 E.8886 Write the following numbers using scientifc notation : A 56.8 × 10 2 b 0.0023 × 10 − 7 c 123.45 × 10 − 4 d 0.091 × 10 2 17. Problems E.8882 1 Arrange the following integers in ascending order : 2 ; 2 2 ; 2 3 ; 2 4 2 Arrange the following numbers in ascending order : 1 2 ; 1 2 2 ; 1 2 3 ; 1 2 4 E.8881 ABCD is a rectangle that has area 2 11 cm 2 and such that : AB = 2 5 cm . 1 Calculate AD into cm . The result will be given as a power of 2 . 2 Calculate the perimeter of ABCD into cm . The answer will be given as a × 2 6 où a is an integer. https://chingmath.fr chapExoCorrec/8868 sacados/8868 chapExoCorrec/8869 sacados/8869 chapExoCorrec/8871 sacados/8871 chapExoCorrec/8872 sacados/8872 chapExoCorrec/8873 sacados/8873 chapExoCorrec/8885 sacados/8885 chapExoCorrec/4802 sacados/4802 chapExoCorrec/8952 sacados/8952 chapExoCorrec/2036 sacados/2036 chapExoCorrec/8880 sacados/8880 chapExoCorrec/1152 sacados/1152 chapExoCorrec/649 sacados/649 chapExoCorrec/3498 sacados/3498 chapExoCorrec/8886 sacados/8886 chapExoCorrec/8882 sacados/8882 chapExoCorrec/8881 sacados/8881
E.8883 The following two questions are in-dependent : 1 Consider the following sum : S = 3 0 + 3 1 + 3 2 + 3 3 + 3 4 a By which of the following sentences can this sum be translated : The sum of the powers of the first five natural num-bers to the exponent 3. The sum of the first five powers of 3 whose exponent is a natural number. b Show that S is the square of an integer whose value we will specify. 2 Find n ∈ N that checks : 10 n =100 100 18. Addition of powers of 10 E.2041 Perform the following operations : (hint : transform numbers to the same power of 10) a 3 × 10 7 + 5 × 10 8 b 8 × 10 5 + 24 × 10 4 c 52.1 × 10 − 4 + 18 × 10 − 6 d 22.4 × 10 15 − 2240 × 10 13 e 30.9 × 10 − 6 + 0.09 × 10 − 4 f 10 − 10 + 10 − 11 E.2050 Perform the following operations : (hint : transform numbers to the same power of 10) a 2 × 10 2 + 3 × 10 4 b 3 × 10 − 2 + 3 × 10 − 3 c 8 × 10 5 − 24 × 10 4 d 0.6 × 10 − 4 + 1 × 10 − 6 e 301 × 10 − 15 − 0.05 × 10 − 13 f 2.4 × 10 − 6 + 1.4 × 10 − 4 E.2060 Perform the following operations : a 3 × 10 − 3 + 2.5 × 10 − 2 b 254 × 10 30 + 78 × 10 33 c 94.1 × 10 − 13 − 0.012 × 10 − 10 E.2156 Carry out the following operations, detailing the steps in your calculations : a 3 × 10 − 1 + 5 × 10 − 4 b 7 × 10 7 − 2 × 10 5 c 35 × 10 15 + 0.09 × 10 18 d 0.05 × 10 − 42 − 4 × 10 − 45 E.8953 Write the following numbers as dec-imals: a 3 × 10 2 + 2 × 10 − 1 + 5 × 10 − 2 b 2 × 10 − 2 + 31 × 10 − 3 c 35 × 10 7 + 54 × 10 9 d 6 × 10 − 8 − 57 × 10 − 9 19. Usmath E.9648 With American notations: to caclulate the power of a ˇ mixed fractions ı, we go through a ˇ improper fractions ı be-fore expressing the result as a ˇ mixed fractions ı. Example : 1 1 5 3 = 1 + 1 5 3 = 5 5 + 1 5 3 = 5 + 1 5 3 = 6 5 3 = 216 125 = 125 + 91 125 = 125 125 + 91 125 = 1 + 91 125 = 1 91 125 Express the powers below as ˇ mixed fractions ı : a 5 1 3 2 b 3 1 7 2 c 3 1 2 3 d 1 1 3 3 20. Share E.8957 Simplify the calculations below to give the result as a power of 10 : a 10 7 × 10 − 9 b 10 − 7 10 7 c 10 8 × 10 − 3 10 − 5 d 10 5 10 × 10 9 21. Unclassified exercises E.7469 Simplify the following expressions : a 2 4 × 2 3 b 5 8 5 3 c 3 2 4 d 3 4 × 9 3 e 4 9 2 5 f 2 5 − 2 4 https://chingmath.fr chapExoCorrec/8883 sacados/8883 chapExoCorrec/2041 sacados/2041 chapExoCorrec/2050 sacados/2050 chapExoCorrec/2060 sacados/2060 chapExoCorrec/2156 sacados/2156 chapExoCorrec/8953 sacados/8953 chapExoCorrec/9648 sacados/9648 chapExoCorrec/8957 sacados/8957 chapExoCorrec/7469 sacados/7469