Grade 9 / Powers 83 exercises (100% corrected)

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ChingQuizz : 3 exercises available for Quizz assessment : 1. Some calculations on the powers E.3497 Perform the following calculations : a 5 3 − 10 2 b (5 2 − 19) × (2 + 3) 2 c 5 0 − 8 0 5 10 + 8 10 d 8 2 − 7 2 + 5 0 E.2173 Write the three numbers be-low as decimals : a 5 2 + 2 2 × 9 b 3 2 4 + 2 2 c 5 × 10 3 − 2 × 10 2 E.9863 Perform the following calculations : A 7 − 4 × 21 × 14 b 15 5 2 + 6 × 3 − 2 E.5088 1 What is the decimal writing of the number 10 5 +1 10 5 ? 2 Antoine uses his calculator to calculate the following number 10 15 +1 10 15 Antony thinks this result is not accurate. Is he right? E.3546 Give the reduced form of each of the following fractions : a 3 4 2 − 1 4 b 9 7 18 5 c 6 10 2 5 × 3 12 − 2 4 3 2 E.4835 Write each of the numbers below in the form a n : a 2 × 3 2 + 2 × 3 2 b 3 15 × 2 10 − 3 13 × 2 10 2. Powers of 10 E.9190 Copy and complete the following blanks correctly: a 351 × 10 14 = 0.351 × 10 ... b 0.045 × 10 − 12 = : : : × 10 − 16 c 54.4 × 10 2 = 0.544 × 10 ... 3. Scientific notations E.2145 Fill in the blanks with the appropri-ate value : a 3 × 10 4 = : : : × 10 2 b 35.1 × 10 2 = 0.351 × 10 ... c 35 × 10 − 24 = : : : × 10 − 25 d 750 × 10 − 9 = 7.5 × 10 ... e 0.005 42 × 10 16 =5.42 × 10 ... f 0.0032 × 10 − 4 = : : : × 10 − 8 E.2035 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.2049 For each question, say whether the equality is true or false : a 0.6512 × 10 4 = 6.512 × 10 5 b 0.0021 × 10 − 2 = 2.1 × 10 − 5 c 5 000 × 10 2 = 5 × 10 − 1 d 561 × 10 7 = 5.61 × 10 9 e 0.000 000 023 × 10 − 1 = 2.3 × 10 − 9 E.2369 Copy each of the equalities, filling them in appropriately : a 145.1 × 10 4 = 0.1451 × 10 ? b 0.074 × 10 2 = : : : × 10 − 1 E.1149 Write the following numbers using scientific notation : A 56.8 × 10 2 b 0.0023 × 10 − 7 c 123.45 × 10 − 4 d 0.091 × 10 2 E.2040 Compare the following pairs of num-bers : a A = 32.5 × 10 5 et B = 0.315 × 10 8 b A = 0.005 × 10 − 5 et B = 502 × 10 − 9 c A = 0.0247 × 10 4 et B = 2401 × 10 − 1 Hint: look up the scientific notation for each https://chingmath.fr chapExoCorrec/3497 sacados/3497 chapExoCorrec/2173 sacados/2173 Extrait Centres Etrangers - Juin 2007 - 3 points chapExoCorrec/9863 sacados/9863 chapExoCorrec/5088 sacados/5088 chapExoCorrec/3546 sacados/3546 chapExoCorrec/4835 sacados/4835 chapExoCorrec/9190 sacados/9190 chapExoCorrec/2145 sacados/2145 chapExoCorrec/2035 sacados/2035 chapExoCorrec/2049 sacados/2049 chapExoCorrec/2369 sacados/2369 chapExoCorrec/1149 sacados/1149 chapExoCorrec/2040 sacados/2040
E.4834 Give the scientific form of the num-bers below : a 4 540 000 b 0.000 054 c 354.1 × 10 11 d 79.8 × 10 − 8 e 0.000 079 × 10 8 f 0.005 2 × 10 − 4 E.618 C = 15 × (10 7 ) 2 × 3 × 10 − 9 Calculate C , give the result in the form a × 10 n and with sci-entific notation. E.11772 Donner l’écriture scientifique des nom-bres suivants : a 0 ; 00023 b 3215 ; 8 × 10 1000 E.11773 Donnez l’écriture scientifique des nom-bres suivants : a 123546 b 5121 ; 1 × 10 780 E.11774 Effectuer les calculs suivants et écrire les résultats avec la notation scientifique: a 3 × 10 4 × 9 × 10 3 b 0 ; 1 × 10 − 5 × 0 ; 7 × 10 − 7 c 12 × 10 − 7 2 4. Scientific Notation and Fractions E.9191 We give : B = 4 × 10 − 2 × 9 × 10 6 6 × 10 7 × 15 × 10 3 2 Give the scientifc notation of B . E.634 Write the following numbers in scientific notation : a 1 ; 5 × 10 − 3 3 × 10 2 b 5 × 10 4 × 42 × 10 2 6 × 10 − 4 E.624 Write the following numbers in scientific notation : a 14 × 10 4 × 75 × 10 − 7 35 × 10 − 3 b 33 × 10 − 3 × 8 × 10 5 2 12 × 10 2 E.4831 Perform the following calculations and write the results using scientific notation : a 3 × 10 4 × 9 × 10 3 b 0.1 × 10 − 5 × 0.7 × 10 − 7 c 12 × 10 − 7 2 d 9 × 10 5 4 × 10 15 e 0.02 × 10 − 3 5 × 10 4 f 126 × 10 15 3 × 10 7 E.1150 Perform the following calculations and write the result in scientific notation : a 8 × 10 5 × 9 × 10 9 6 × 10 4 b 5 × 10 4 × 2 × 10 2 25 × 10 − 4 × 8 × 10 6 5. Powers of positive exponent E.8307 Simplify the writing of the following expressions : a 10 2 × 10 7 b 10 14 × 10 21 c 10 7 10 4 d 10 21 10 14 e 10 4 2 f 10 3 3 E.8306 Simplify the writing of the following expressions : a 3 7 × 3 8 b 5 8 × 5 7 c 3 × 3 11 d 3 8 × 5 8 e 4 12 × 5 12 f 17 5 × 2 5 E.9173 Simplify the writing of the following expressions : A 5 3 × 9 3 b 5 2 × 3 2 c 1.2 3 × 5 3 d 5 4 × 3 4 e 6 2 × 6 3 f 3 5 × 8 5 E.9169 Simplify the writing of the following expressions : a 3 5 3 2 b 8 3 8 2 c 4 5 4 6 d 3 5 3 8 E.9864 Simplify the following expressions : a 9 5 × 3 10 b 8 3 × 4 15 6. Multiplication of powers E.9177 Proposition: let a be a number and n , p any two integers. We have the simplification : a n × a p = a n + p Perform the following calculations : a 5 4 × 5 − 7 b 6 4 × 6 − 4 c 3 5 × 3 − 10 d 5 6 × 5 e 10 30 × 10 − 9 f 5 4 × 5 − 10 https://chingmath.fr chapExoCorrec/4834 sacados/4834 chapExoCorrec/618 sacados/618 chapExoCorrec/11772 sacados/11772 chapExoCorrec/11773 sacados/11773 chapExoCorrec/11774 sacados/11774 chapExoCorrec/9191 sacados/9191 chapExoCorrec/634 sacados/634 extrait du brevet de Pondichery et Madagascar 2005 chapExoCorrec/624 sacados/624 chapExoCorrec/4831 sacados/4831 chapExoCorrec/1150 sacados/1150 chapExoCorrec/8307 sacados/8307 chapExoCorrec/8306 sacados/8306 chapExoCorrec/9173 sacados/9173 chapExoCorrec/9169 sacados/9169 chapExoCorrec/9864 sacados/9864 chapExoCorrec/9177 sacados/9177
E.4819 Simplify the writing of the following powers : A 5 2 × 5 5 b 7 4 × 7 − 7 c 5 × 5 − 4 d 8 5 × 8 − 3 × 8 − 2 e 5 20 × 5 − 9 E.3385 Simplify as much as possible the writing of the following expressions. The result will be given as a power: A 6 0 b 7 5 × 7 − 3 c 3 − 4 × 3 5 E.1148 Simplify the writing of the following powers : a 2 − 4 × 3 − 4 b 5 4 × 3 4 c 5.6 10 × 10 10 E.9186 Copy and fill in the following expo-nents in the following equations : a 2 × 2 ? = 2 7 b 4 7 × 4 ? = 4 3 c 7 4 × 7 ? = 1 d 5 2 × 5 ? = 5 − 2 e 3 5 × : : : = 3 − 2 f 12 × : : : = 3 × 2 8 E.9174 Perform the following calculations and give the result in simplified form : a 12 3 × 12 − 15 × 12 4 b 5 12 × 8 16 × 8 − 4 c 5 3 × 5 2 × 5 − 5 E.3536 Simplify the writing of the following expressions : a 5.2 4 × 10 000 b 84 5 × 0.000 01 E.9182 Simplify as much as possible the writing of the following expressions. The result will be given as a power: a 15 4 × 5 − 4 b 4 8 × 3 − 8 c 32 5 × 4 − 5 E.9181 a and b represent real numbers ; n and m are relative integers. Express each of the following expressions in the form c p : a a 8 × a 5 b a 3 × a − 14 c 3 n × 5 n d 4 n × 2 2 · n E.9183 Write the following expression in the form a n : 5 4 × 10 − 2 × 2 4 7. Power division E.9176 Perform the following calculations : a 10 120 10 − 99 b 5 8 5 − 8 c 7 13 7 − 13 d 7 2 7 4 e 7 2 7 − 4 f 10 20 10 − 20 E.4781 Proposition: let a be a number and n , p any two integers. We have the simplification : a n a p = a n − p Simplify the writing of the following expressions : a 5 2 5 3 b 7 − 3 7 5 c 12 22 12 − 12 d 2 − 5 2 − 12 e 3 7 3 4 f 8 3 8 − 5 g 3 12 3 5 h 7 − 9 7 10 E.9178 Simplify the following entries as much as possible : a 12 11 3 11 b 5 11 15 11 c 27 7 9 7 E.9171 Simplify the following expressions as much as possible. The result will be given as a power: a 3 2 3 5 b 5 − 4 5 2 c 6 3 6 3 d 5 2 5 − 6 E.9184 Copy and fill in the following expo-nents in the following equations : a 5 7 5 ? = 5 5 b 5 2 5 ? = 5 6 E.3528 a and b represent real numbers ; n and m relative integers. Express each of the following expres-sions in the form c p : a a 5 a 9 d a 12 a − 5 E.9185 Complete each of the following equa-tions correctly: a : : : × 7 4 7 8 = 7 − 12 b : : : 7 3 = 7 4 c 5 − 3 : : : = 5 − 8 d : : : 2 − 5 = 2 15 8. Powers of powers E.9172 Proposition: let a be a number and n , p any two integers. We have the simplification : a n p = a n × p Simplify the writing of the following expressions : a 3 2 7 b 11 5 − 4 c 5 2 8 E.9180 a and b represent real numbers ; n and m are relative integers. Express each of the following expressions in the form c p : a a 5 3 b a − 2 5 c a − 4 − 3 https://chingmath.fr chapExoCorrec/4819 sacados/4819 chapExoCorrec/3385 sacados/3385 chapExoCorrec/1148 sacados/1148 chapExoCorrec/9186 sacados/9186 chapExoCorrec/9174 sacados/9174 chapExoCorrec/3536 sacados/3536 chapExoCorrec/9182 sacados/9182 chapExoCorrec/9181 sacados/9181 chapExoCorrec/9183 sacados/9183 chapExoCorrec/9176 sacados/9176 chapExoCorrec/4781 sacados/4781 chapExoCorrec/9178 sacados/9178 chapExoCorrec/9171 sacados/9171 chapExoCorrec/9184 sacados/9184 chapExoCorrec/3528 sacados/3528 chapExoCorrec/9185 sacados/9185 chapExoCorrec/9172 sacados/9172 chapExoCorrec/9180 sacados/9180
9. Algebraic operations on positive numbers E.9170 Complete the blanks to achieve equality: a 3 5 × 9 = 3 ? b 4 4 × 2 2 = 2 ? c 8 2 × 4 5 = 2 ? E.1151 Copy and complete the following exponents in the following equations : a 2 × 2 ? = 2 7 b 4 7 × 4 ? = 4 3 c 5 7 5 ? = 5 5 d 5 2 5 ? = 5 6 e 7 4 × 7 ? = 1 f 5 2 × 5 ? = 5 − 2 E.3386 Copy the following calculations and replace the ˇ?ı with the missing exponent : a 6 ? × 6 7 = 6 9 b 6 ? × 6 9 = 6 7 c 5 − 3 × 5 ? = 5 − 6 d 3 2 × 2 ? = (3 × 2) 2 e 156 ? = 1 f 3 2 × 2 ? = 6 2 E.3522 Complete each of the following equa-tions correctly: a 5 16 × : : : = 10 16 b 8 × 5 3 = : : : 3 c 27 × : : : = 3 15 E.1143 Copy and complete the exponents appropriately so that the equalities are true : a 2 6 ... = 2 60 b 16 5 = : : : 10 E.3523 Write each of the products in the form a n où a and n are relative integers : a 5 12 × 3 2 6 b 2 4 3 × 5 12 E.3502 Simplify each of the following calcu-lations into the form a p où p is a relative integer: a 5 8 7 6 × 5 − 2 b 8 2 × 8 − 9 8 − 4 c 10 4 × 5 7 2 4 E.3520 1 Consider the following two integers defined in terms of the positive integer n by: A = 2 (2 n ) ; B = 2 2 n a Determine the value of the integers A and B for : n = 1 ; n = 2 b What can we say about the numbers A and B ? 2 a Determine the value of A and B for n =3 and for n =0 . b What can be said about the integers A and B ? E.9175 Simplify the writing of the following powers : a 2 10 + 2 10 b 2 31 − 2 30 c 3 7 + 2 × 3 7 10. Sign of a product E.9179 Give the sign of each of the following expressions : a 3 − 5 b − 2 4 c − 8 − 3 d ( − 3) 2 e ( − 3) − 2 E.3496 Give the sign of each of the following numbers : a ( − 2.7) 2 b 5.2 − 2 c ( − 3) 31 d 5.2 24 e ( − 1) − 5 f ( − 5.2) 52 E.2034 Determine the sign of each of the products below : a ( − 2) 2 × 2 − 3 b ( − 3) 5 × ( − 2) 4 c ( − 1) 10 × ( − 2) − 2 d ( − 4) 7 × 2 − 3 e ( − 1) − 9 × ( − 2) f ( − 2) 5 × ( − 3) × ( − 2) − 2 E.2052 Determine the sign of each of the products below : a 2 − 3 × 3 − 10 b ( − 2) 2 × ( − 2) − 3 c ( − 2) − 5 × 3 d ( − 1) − 5 × ( − 3) 4 E.2058 1 Justify that the following calculation has its negative re-sult : ( − 2) 5 × (7) − 3 2 Determine the sign of each of the calculations below : a ( − 2) − 7 × ( − 7 2 ) b − 3 × 5 − 3 c ( − 3) 101 × ( − 2) − 50 11 − 53 d ( − 2) − 5 × ( − 9) E.9192 Determine the sign of each of the products below : a ( − 1) − 5 × 7 − 2 ( − 2) 5 b ( − 1) 5 × ( − 2) − 4 ( − 3) − 6 c ( − 1) − 5 × 7 − 2 ( − 2) 5 11. Relative numbers and power operations E.3521 1 Perform the following : a − 3 4 b − 3 4 c − 3 4 2 Perform the following operations, taking into account the priority of the operations : https://chingmath.fr chapExoCorrec/9170 sacados/9170 chapExoCorrec/1151 sacados/1151 chapExoCorrec/3386 sacados/3386 chapExoCorrec/3522 sacados/3522 chapExoCorrec/1143 sacados/1143 chapExoCorrec/3523 sacados/3523 chapExoCorrec/3502 sacados/3502 chapExoCorrec/3520 sacados/3520 chapExoCorrec/9175 sacados/9175 chapExoCorrec/9179 sacados/9179 chapExoCorrec/3496 sacados/3496 chapExoCorrec/2034 sacados/2034 chapExoCorrec/2052 sacados/2052 chapExoCorrec/2058 sacados/2058 chapExoCorrec/9192 sacados/9192 chapExoCorrec/3521 sacados/3521
a ( − 3) 2 × − 3 2 b − 5 − 2 × − 5 2 c − 3 3 × − 3 − 4 d − 4 6 4 E.3501 Simplify each of the following calcu-lations into the form a p où p is a relative integer: a 5 3 × 5 8 b ( − 3) 5 × 3 7 c 8 − 12 × 8 × 8 3 d 6 0 × 6 − 6 e ( − 5) − 4 × 5 12 f 5 − 13 × 5 E.4808 Simplify the writing of the following expressions : a ( − 2) 6 b ( − 4) − 3 × 4 5 c − 3 5 × 3 − 2 × ( − 3) − 7 d ( − 2) 5 × ( − 6) 5 E.5060 Determine the sign of each of the products below : a ( − 2) 2 × 2 − 3 b ( − 3) 5 × ( − 2) 4 c ( − 1) 10 × ( − 2) − 2 d ( − 4) 7 × 2 − 3 E.9189 Simplify the writing of the following expressions : a 7 − 8 − 7 − 5 b ( − 3) 7 − 3 5 c − ( − 11) 4 55 4 E.4832 Simplify the writing of the following expressions : a ( − 5) 4 × 5 − 8 b 3 − 3 × ( − 3) − 3 c ( − 5) 2 × ( − 5) 7 E.3026 Simplify the writing of the following expressions : a ( − 3) 4 × 3 − 10 b − 5 − 4 × ( − 5) 7 × 5 − 4 c 25 × ( − 3) 2 3 E.9187 Simplify the writing of the following expressions : a ( − 7) 7 7 5 × ( − 7) 2 b ( − 2) 5 × 6 5 ( − 12) − 3 c ( − 5) − 7 − 5 4 × ( − 5) − 4 E.9188 Simplify the writing of the following expressions : a 3 − 5 × ( − 3) − 4 − 3 − 5 b ( − 2) 4 × 4 2 2 8 12. Problems E.3500 1 Show that a day contains 8.64 × 10 4 seconds. 2 The speed of light is 3 × 10 5 km = s . Indication : results will be indicated in scientific writing. a How many kilometers does light travel in one day? b Convert this length into meters. E.3525 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.3549 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. E.6283 A ball is dropped from a height of 1 meter. With each bounce, it bounces from 3 4 the height from which it fell. How high does the ball reach on the fifth bounce? Round to the nearest cm . E.9194 Find n ∈ N that checks : 10 n = 100 100 E.3531 Consider the triangle ABC admit-ting the following measures : AB = 3 × 5 3 ; AC = 5 4 ; BC = 4 × 5 3 Show that the triangle ABC is a right triangle. We will spec-ify its characteristics. E.5694 Lea observes a bamboo cell under a microscope at noon. After an hour, the cell has split in two. We then have two cells. After two hours, these two cells have divided into two. Lea records the results of her observation every hour. At what time will she note, for the first time, more than 200 cells? Leave all traces of research apparent. Even if the work is not completed, it will be reflected in the grading. E.3526 Consider the following sum : S = 3 0 +3 1 +3 2 +3 3 +3 4 1 By which of the following sentences can this sum be trans-lated : The sum of the powers of the first five natural numbers to the exponent 3. The sum of the first five powers of 3 whose exponent is a natural number. 2 Establish that S is the square of an integer whose value we will specify. 13. Problems and geometry https://chingmath.fr chapExoCorrec/3501 sacados/3501 chapExoCorrec/4808 sacados/4808 chapExoCorrec/5060 sacados/5060 chapExoCorrec/9189 sacados/9189 chapExoCorrec/4832 sacados/4832 chapExoCorrec/3026 sacados/3026 chapExoCorrec/9187 sacados/9187 chapExoCorrec/9188 sacados/9188 chapExoCorrec/3500 sacados/3500 chapExoCorrec/3525 sacados/3525 chapExoCorrec/3549 sacados/3549 chapExoCorrec/6283 sacados/6283 Asie Juin 2014 3 points chapExoCorrec/9194 sacados/9194 chapExoCorrec/3531 sacados/3531 chapExoCorrec/5694 sacados/5694 chapExoCorrec/3526 sacados/3526
ABCMN2×1033;2×1011400×10102;5×104 E.9193 The following configuration is con-sidered : The straight lines ( BM ) and ( CN ) are secant at the point A . Show that the lines ( BC ) and ( MN ) are parallel. 14. Unclassified exercises E.3387 1 Give the truncation to the nearest thousandth of A = 25.3467 2 Give the rounding to the nearest 10 − 2 of : B = 75.2445 ; C = 0.3596 3 Give a frame to the nearest tenth of D =23.74 E.1146 1 As a reminder about relative numbers, complete the ta-ble below : m n m + n m − n m × n m = n 4 8 − 4 2 − 5 4 − 1 − 3 2 Simplify the following quotients : a 7 9 7 4 b 3 12 3 7 c 4 5 4 9 d 8 2 8 9 3 Complete the following table : a m n Simplification of a m a n Writing of a m − n 7 9 4 3 12 7 4 5 9 8 2 9 12 5 12 Definition: the power of a negative exponent of a number is defined by the two equalities: a − 1 = 1 a ; a − n = 1 a n 4 Simplify the following expressions : a 3 5 3 6 b 5 12 5 22 c 7 15 7 2 d 9 5 9 16 E.2087 Compare the following numbers, giving the scientific form of each : A 52.5 × 10 12 et 5.12 × 10 14 b 3.1 × 10 − 9 et 0.0301 × 10 − 7 c 74.32 × 10 15 et 0.081 × 10 18 https://chingmath.fr chapExoCorrec/9193 sacados/9193 ABCMN2×1033;2×1011400×10102;5×104 chapExoCorrec/3387 sacados/3387 chapExoCorrec/1146 sacados/1146 chapExoCorrec/2087 sacados/2087