Grade 10 / Powers 53 exercises (100% corrected)

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104106107101010410510110510−110−210−310−4 ChingQuizz : 8 exercises available for Quizz assessment : 1. Operation on powers of ten of positive exponent E.8303 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 2. Operation on powers of positive exponent E.8304 Simplify the following powers : a 3 × 3 5 b 7 5 × 7 9 c 12 13 × 12 5 d 5 8 5 3 e 13 15 13 7 f 7 12 7 5 E.8305 Simplify the following powers : a 7 5 × 7 9 b 5 2 × 5 13 c 7 4 × 7 5 × 7 9 d 6 8 6 7 e 12 8 12 4 f 3 5 × 2 5 E.8302 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 4 5 4 6 g 3 5 3 8 h 3 2 × 5 2 i 4 3 × 5 3 E.271 The following two questions are inde-pendent : 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 inte-gers to 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 will be specified. 2 Find the integer n ∈ N verifying equality: 10 n =100 100 3. Operation on powers of ten E.8298 1 Using the calculator, connect the numbers with the same value : 2 What conjecture can be made? E.8299 Perform the following calculations : a 10 2 × 10 − 1 × 10 − 2 b 10 3 × 10 − 3 10 5 c 10 − 7 10 − 7 d 10 − 5 × 10 4 10 5 e 10 2 × 10 − 4 2 × 10 − 4 f 10 3 10 − 2 4 4. Operation on powers E.8301 Simplify 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/8303 sacados/8303 chapExoCorrec/8304 sacados/8304 chapExoCorrec/8305 sacados/8305 chapExoCorrec/8302 sacados/8302 chapExoCorrec/271 sacados/271 chapExoCorrec/8298 sacados/8298 104106107101010410510110510−110−210−310−4 chapExoCorrec/8299 sacados/8299 chapExoCorrec/8301 sacados/8301
E.244 Determine the sign of each of the following operations : a ( − 7) 8 b − 7 8 c 10 − 5 d − 2 6 e − 4 − 7 f ( − 4) 7 g ( − 3 − 4 ) 5 E.8387 Determine the simplified form of each of the following expressions : a 2 5 × 2 − 8 b 5 4 × 5 2 5 9 c 2 4 5 3 × 5 9 2 E.8300 Simplify the following expressions as much as possible. 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.4419 Simplify the following calculations : a 2 5 × 3 4 × 3 2 × 2 − 8 b 2 5 × 3 4 × 5 2 2 8 × 3 3 × 5 4 c 2 3 × 3 4 3 3 6 E.8264 Determine the simplified form of each of the following expressions : a 2 4 × 2 10 2 7 b 2 4 × 2 × 7 4 2 c 2 4 7 2 2 5 7 9 E.247 Give the simplified form of the ex-pressions below : a 2 4 × 2 − 5 b a 5 × a 4 2 c a 4 × b − 5 a 7 × b − 3 d 2 3 − 3 × 5 7 × 2 9 E.2700 Simplify each of the expressions be-low where a and b are two non-zero numbers : a a 2 × b − 3 × a 5 b a 5 × a 3 × b − 2 5 a − 7 × b 5 c a 6 × a 6 d √ a 52 5. Powers and irreducible fractions E.8249 Express the rational numbers (be-longing to Q ) below in their irreducible form : a 2 5 × 3 4 × 5 × 7 2 2 6 × 3 4 × 7 b 4 × 9 × 25 2 4 × 3 × 5 E.2351 Perform the following calcu-lations and give their results as irreducible fractions. a 1 3 − 1 5 ÷ 2 5 b 4 7 − 1 7 × 5 3 c 5 7 2 − 2 7 d 12 × 10 − 3 × 4 3 × 10 7 16 × 10 2 E.633 Calculate and give the result as an irreducible fraction : A = 26 7 − 22 7 × 10 33 ; B = 7 × 10 35 49 × 10 34 E.8388 Perform the following calculations, giving the results in simplified form : a 5 3 + 3 4 × 42 58 b 1 + 1 3 5 6 − 5 2 c 2 3 × 10 4 × 2 5 × 10 9 2 7 × 10 13 E.9563 Give the simplified forms of the fol-lowing expressions : a 15 × 10 5 × 12 × 10 − 14 6 × 10 7 × 20 × 10 12 b 5 × 10 − 2 2 √ 9 × 10 4 6. Power and decomposition into products of prime factors E.9567 Determine the product of prime fac-tors decomposition of each of the numbers below : a 14 5 × 4 9 × 49 2 b 9 4 × 3 8 × 2 4 × 6 2 E.2699 Simplify the writing of each of the ex-pressions below to obtain a writing of the form 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers : a 75 × 4 6 × 14 − 5 b 18 × 15 2 × 12 4 E.1780 Write the following integers in the form 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers. a (16 + 2) 5 × 14 2 − 1 × 21 − 2 7. Powers, fractions and decomposition https://chingmath.fr chapExoCorrec/244 sacados/244 chapExoCorrec/8387 sacados/8387 chapExoCorrec/8300 sacados/8300 chapExoCorrec/4419 sacados/4419 chapExoCorrec/8264 sacados/8264 chapExoCorrec/247 sacados/247 chapExoCorrec/2700 sacados/2700 chapExoCorrec/8249 sacados/8249 chapExoCorrec/2351 sacados/2351 Brevet blanc Lome 2011 chapExoCorrec/633 sacados/633 Martinique - Septembre 2002 - 3 points chapExoCorrec/8388 sacados/8388 chapExoCorrec/9563 sacados/9563 chapExoCorrec/9567 sacados/9567 chapExoCorrec/2699 sacados/2699 chapExoCorrec/1780 sacados/1780
E.9564 Simplify the writing of the following numbers : a 45 × 8 − 3 14 2 × 20 2 b 6 10 × 5 4 10 − 3 × 2 5 c 12 7 × 15 4 10 3 × 21 − 4 Hint: results will be reported as 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers. E.257 Write the following numbers in the form 2 n × 3 m × 5 k where the numbers n , m , k are relative inte-gers. a 6 10 × 5 3 × 10 2 15 7 × 2 3 b ( − 3) 3 × 15 2 × ( − 4) 3 16 2 × ( − 9) 2 Hint: we will indicate the results in the form 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers. E.245 Transform each of the calculations below to obtain an entry of the form : 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers : a 6 − 4 × 12 2 × (5 3 ) − 2 (30 × 5 2 ) 2 b ( − 16) 2 × ( − 5 3 ) 2 × ( − 27) 5 ( − 21) 4 × 10 E.9568 Write the following integers in the form 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers. a 3 × 6 5 × 10 4 4 5 × 9 7 b ( − 10) 3 × 42 2 × 12 − 11 6 4 × ( − 35) − 9 E.242 Write the following numbers in the form 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers. a 2 5 × 15 − 2 × 14 2 7 − 5 × 9 4 b 10 4 × 6 − 8 35 5 2 c 10 4 + 10 4 √ 7 4 8. Scientific writing E.8265 Write each of the numbers below in the form 2 m × 3 m × 5 p × 7 q with n , m , p , q relative integers. A 6 5 × 15 4 × 14 − 5 b 2 5 × 7 − 2 × 10 4 E.4341 Give the scientific form of the fol-lowing numbers : a 546.7 × 10 9 b 0.045 × 10 − 3 c 87.5 × 10 − 4 y E.2693 Give the scientifc notation of the following numbers : a 123546 b 5121.1 × 10 780 E.9561 Give the scientific form of the fol-lowing expressions : A 354.78 × 10 − 19 b 3 × 10 2 × 2 5 × 10 − 4 − 3 9. Scientific writing, powers and fractions E.248 1 In physics, many constants are used during calculations. Here are just a few : a La gravity: g = 980.665 × 10 − 2 m · s − 2 b Le Avogadro number: N a = 6022.045 × 10 20 mol − 1 c La speed of light : c = 299792458 m · s − 1 Express each of these constants using scientific notation. 2 Astronomers use, as a unit, the light-year. One light-year is equivalent to the number of kilometers light travels in 365.25 days. Express this distance in kilometers using scientific notation (Use constant c ) . E.621 Consider the two numbers A and B : A = 7 5 + 3 5 × 11 6 ; B = 4 × 10 14 × 12 3 × 10 11 1 Calculate and give A in irreducible fraction form. 2 Give the scientific writing of B . E.5180 Consider the three numbers below : A = 3 − 2 3 4 3 × 7 ; B = 49 × 10 3 × 6 × 10 − 10 14 × 10 − 2 ; C = 5 − 3 4 3 + 6 × 5 Answer the following questions, specifying the various stages of your calculations. 1 Write the number A below as an irreducible fraction. 2 Give the scientifc notation of the number B . 3 Using a calculator, give the approximate value of the number C to the nearest hundredth. E.639 Calculate the following numbers and put A and B as irreducible fractions the results and give the result of C in scientific writing: A = 1 − 2 3 + 1 4 ; B = 3 − 5 2 1 + 1 5 ; C = 7 × (10 5 ) 2 × 10 − 3 35 × 10 3 E.266 Simplify the fraction below and give its scientific form : (6 × 10) 2 × 3 2 × 10 − 4 3 3 × 10 12 E.9566 Write the scientific form of the fol-lowing numbers : a 14 × 10 4 × 75 × 10 − 7 35 × 10 − 3 b 33 × 10 − 3 × 8 × 10 5 2 12 × 10 2 E.9565 Write each of the numbers below in the form 2 m × 3 m × 5 p × 7 q with n , m , p , q relative integers. a 2 5 × 5 − 3 3 4 × 21 − 7 b 10 2 × 21 − 2 2 3 3 + 3 3 https://chingmath.fr chapExoCorrec/9564 sacados/9564 chapExoCorrec/257 sacados/257 chapExoCorrec/245 sacados/245 chapExoCorrec/9568 sacados/9568 chapExoCorrec/242 sacados/242 chapExoCorrec/8265 sacados/8265 chapExoCorrec/4341 sacados/4341 chapExoCorrec/2693 sacados/2693 chapExoCorrec/9561 sacados/9561 chapExoCorrec/248 sacados/248 chapExoCorrec/621 sacados/621 Lyon - 2002 - 2 points chapExoCorrec/5180 sacados/5180 chapExoCorrec/639 sacados/639 chapExoCorrec/266 sacados/266 chapExoCorrec/9566 sacados/9566 chapExoCorrec/9565 sacados/9565
ABC21023×21005×2100 10. Factoring and powers E.8266 Establish the equations below : a 9 × 10 5 + 4 × 10 4 = 94 × 10 4 b 2 × 3 3 + 3 3 = 3 4 c 3 × 10 − 2 − 3 × 10 − 3 =27 × 10 − 3 d 2 15 × 3 12 − 2 13 × 3 12 =6 13 E.3524 For each calculation below, carry out a factorization to simplify the writing of the expression : a 3 5 + 3 7 b 3 × 5 2 + 2 × 5 4 c 3 10 − 2 × 3 9 d 5 × 8 5 − 5 × 8 4 e 10 20 + 10 21 + 10 22 f 6 10 3 9 + 4 10 2 8 E.9562 Perform the following operations and give their simplified forms : a 13 × 10 − 5 + 0.024 × 10 − 2 b 4 4 × 4 4 E.9572 Using factorization, simplify the fol-lowing expressions : a 25 × 10 35 + 12 × 10 33 b 2 10 × 5 4 − 5 4 × 2 9 E.9570 Using factorization, give a simplified form of the following expressions : a 3 × 10 14 + 5 × 10 15 b 3 10 − 9 6 E.8319 Simplify the following calculations : a 5 2 × 2 4 2 × 5 × 2 4 b 3 15 + 3 15 2 5 × 3 10 Note: The results should be given in the form 2 m × 3 n × 5 p × 7 q where m , n , p , q are relative integers. 11. Factoring, powers and scientific writing E.622 Calculate, giving the result in scientific notation : C = 153 × 10 − 4 + 32 × 10 − 3 − 16 × 10 − 5 E.2175 1 Give the scientifc notation of the following numbers : a 351 × 10 − 41 b 0.00124 × 10 14 2 Perform the calculation below and give the scientifc no-tation of the result : 5 × 10 − 43 + 10 − 41 × 5 × 10 23 E.3535 We represent by n a non-zero natural number. 1 Demonstrate the following equalities: a 3 2 n = 9 n b 2 n +1 − 2 n = 2 n 2 a Establish the following equality: 20 n − 10 n = 2 n − 1 × 10 n b Determine the scientifc notation of the number A de-fined by: A = 20 12 − 10 12 12. Problem E.8389 Consider the triangle ABC shown below where : AB = 5 × 2 100 ; AC = 3 × 2 100 ; BC = 2 102 Show that the triangle ABC is right-angled at C . 13. Unclassified exercises E.5109 Copy and complete the following equa-tions : a 524.2 × 10 − 12 = 0.5242 × : : : b 0.054 × 10 5 = : : : × 10 3 E.9569 Write each of the following expressions in the form a n : https://chingmath.fr chapExoCorrec/8266 sacados/8266 chapExoCorrec/3524 sacados/3524 chapExoCorrec/9562 sacados/9562 chapExoCorrec/9572 sacados/9572 chapExoCorrec/9570 sacados/9570 chapExoCorrec/8319 sacados/8319 chapExoCorrec/622 sacados/622 chapExoCorrec/2175 sacados/2175 chapExoCorrec/3535 sacados/3535 chapExoCorrec/8389 sacados/8389 ABC21023×21005×2100 chapExoCorrec/5109 sacados/5109 chapExoCorrec/9569 sacados/9569
a 5 4 × 5 − 6 b 7 4 × 3 4 c 5 4 2 6 × 2 10 d 1.2 5 × 6 − 4 × 5 5 e 3 − 5 × 5 5 f 8 2 2 5 E.3555 Write each of the following numbers in the form a p où a is a whole number or in fractional writing and p is a relative integer: a 7 5 × 7 − 4 b 5 2 − 2 c 5 4 × 7 4 d 3 10 × 3 − 15 × 5 5 E.9571 Write each of the following numbers in the form a p où a is a whole number or in fractional writing and p is a relative integer: a 7 5 × 7 − 4 b 5 2 − 2 c 5 4 × 7 4 d 3 10 × 3 − 15 × 5 5 https://chingmath.fr chapExoCorrec/3555 sacados/3555 chapExoCorrec/9571 sacados/9571