Grade 8 Exponents and Powers

Transcription

1 ID : ae-8-exponents-and-powers [] Grade 8 Exponents and Powers For more such worksheets visit Answer t he quest ions () If the mean of three numbers a, b and c is 6, then f ind the value of. (2) Write f ollowing numbers in standard f orm A) 65,000,000 B) C) D) (3) ? (4) If, and, f ind the value of xyz. (5) Write f ollowing numbers in usual f orm A) B) C) D) (6) If 4 x x 3 4, then what is the value of 64 x? (7) Simplif y 243 3/5. Choose correct answer(s) f rom given choice (8)? a b c d (9) What is the unit's digit in (267) 3 X (267) 00? a. b. 9 c. 3 d. 7 (C) 206 Edugain (

2 ID : ae-8-exponents-and-powers [2] (0) 32-4/5? a. 8 b. 64 c. 32 d. 6 () What is the value of 7973 x ? a b. 3 8 c. 4 8 d. 3 7 (2) 3-3 (-4) 2? a. 6 c. -6 b. 432 d. 6 (3) What is the value of (-4) -6? a. c b d (4) Simplif y (243) -3/5 3? a. - b. c. 9 d. - 9 (5) Simplif y. a. b. c. d. (C) 206 Edugain (

3 206 Edugain ( All Rights Reserved ID : ae-8-exponents-and-powers [3] Many more such worksheets can be generated at (C) 206 Edugain (

4 Answers ID : ae-8-exponents-and-powers [4] () 5 6 Step It is given that mean of three numbers a, b and c is 6. a + b + c 6 3 a + b + c 3 6 a + b + c 8 5 8/3 5 6 (2) A) Step First part of the standard f ormat is a number between and 0, theref ore f or given number this should 6.5 Now we can see that 6.5 needs to be multiplied by 0 7, such that multiplication gives us required number Theref ore given number in standard f orm will be B) Step First part of the standard f ormat is a number between and 0, theref ore f or given number this should 8.2 Now we can see that 8.2 needs to be multiplied by 0-7, such that multiplication gives us required number Theref ore given number in standard f orm will be (C) 206 Edugain (

5 C) ID : ae-8-exponents-and-powers [5] Step First part of the standard f ormat is a number between and 0, theref ore f or given number this should 7.5 Now we can see that 7.5 needs to be multiplied by 0-3, such that multiplication gives us required number Theref ore given number in standard f orm will be D) Step First part of the standard f ormat is a number between and 0, theref ore f or given number this should 4.6 Now we can see that 4.6 needs to be multiplied by 0-5, such that multiplication gives us required number Theref ore given number in standard f orm will be (3) Step We have been asked to f ind the value of ( ) Theref ore, the value of is (C) 206 Edugain (

6 ID : ae-8-exponents-and-powers [6] (4) Step According to the question, if a x 3 b, b y 3 c and c z 3 a, we have been asked to f ind the value of xyz. a x 3 b a x (b) /3 a 3x b and b y 3 c b y (c) /3 b 3y c and c z 3 a c z (a) /3 c 3z a Put the value of c in c 3z a a (b 3y ) 3z a b 3 3 yz a b 9yz Now put the value of b a (a 3x ) 9yz a a 3 9 xyz a a xyz Step 4 On comparing powers in above equation, xyz xyz Step 5 Theref ore, the value of xyz is. (C) 206 Edugain (

7 (5) A) ID : ae-8-exponents-and-powers [7] Step We have been asked to f ind the usual f orm of the number Theref ore, the usual f orm of is B) Step We have been asked to f ind the usual f orm of the number Theref ore, the usual f orm of is C) 4,000,000 Step We have been asked to f ind the usual f orm of the number ,000,000 Theref ore, the usual f orm of is 4,000,000. (C) 206 Edugain (

8 D) 9,000,000 ID : ae-8-exponents-and-powers [8] Step We have been asked to f ind the usual f orm of the number ,000,000 Theref ore, the usual f orm of is 9,000,000. (6) 728 (7) Step We have been asked to f ind the value of 243 3/5. Given, x 243 3/5 ( ) 3/5 3 5 (3/5) 3 3 Theref ore, the value of 243 3/5 is. (C) 206 Edugain (

9 (8) a Step We have been asked to f ind the value of. ID : ae-8-exponents-and-powers [9] ( -2 4 ) -3 ( -4 3 ) 2 ( 4-2 ) 3 ( -4 3 ) Theref ore, the value of is (C) 206 Edugain (

10 (9) d. 7 ID : ae-8-exponents-and-powers [0] Step (267) 3 (267) 00 (267) 23 Let's see the pattern when 7 is multiplied, Last digit of 7 7 Last digit of 7 2 (last digit of 7x7) 9 Last digit of 7 3 (last digit of 9x7) 3 Last digit of 7 4 (last digit of 3x7) Last digit of 7 5 (last digit of x7) 7 Last digit of 7 6 (last digit of 7x7) 9 Last digit of 7 7 (last digit of 9x7) 3 Last digit of 7 8 (last digit of 3x7) So we can see that last digit repeats af ter every power of 4. Now remainder of 23/4 Theref ore last of digit of (267) 23 last digit of 7 7 Step 4 Theref ore, the unit's digit in (267) 3 (267) 00 is 7. (C) 206 Edugain (

11 (0) d. 6 Step We have been asked to f ind the value of 32-4/ /5 32 4/5 ID : ae-8-exponents-and-powers [] ( ) 4/ / Theref ore, the value of 32-4/5 is 6. (C) 206 Edugain (

12 () ID : ae-8-exponents-and-powers [2] d. 3 7 Step We can see that base of denominator (i.e. 2) is equal to products of bases of numerator (i.e. 7 and 3). Theref ore if we write 2 as multiplication of 7 and 3 in denominator, some part will cancel out and we should be able to simplif y it. Theref ore, x (7 3) [since (xy) n x n y n ] ( ) 7 ( ) Theref ore, the value of 7973 x is 3 7. (C) 206 Edugain (

13 (2) a. 6 ID : ae-8-exponents-and-powers [3] Step Let's look at the f ollowing f acts bef ore solving the question. Fact : If the exponent of a negative integer is odd, the resultant is a negative number. For example, (-) 2 Fact 2: If the exponent of a negative integer is even, the resultant is a positive number. For example, (-) 3 - Fact 3: If the exponent of an integer is negative, the resultant is the reciprocal of the integer with the exponent made positive. For example, (2) -3 (2) 3 we have to f ind the value of 3-3 (-4) 2, which is equals to ( ) ((-4) 2 ) 3 3 ( ) ((-4) (-4) ) ( ) (6) 6 Thus, the value of 3-3 (-4) 2 is 6. (C) 206 Edugain (

14 (3) a ID : ae-8-exponents-and-powers [4] Step We have been asked to f ind the value of (-4) -6. (-4) -6 (-4) 6 (-4) (-4) (-4) (-4) (-4) (-4) 4096 Theref ore, the value of (-4) -6 is (4) c. 9 Step Lets f irst f ind prime f actors of 243, (243) -3/5 3 ( ) -3/5 3 (3 5 ) -3/5 3 (3) (3) 3 9 (C) 206 Edugain (

15 (5) c. ID : ae-8-exponents-and-powers [5] Step The denominator of the f raction can be simplif ied, if we multiply it by ( 6 + 5). Theref ore, let's multiply both numerator and denominator by ( 6 + 5) ( 6 + 5) 2 ( 6) 2 - ( 5) 2 ( 6)2 + ( 5) Theref ore, the simplif ication of is (C) 206 Edugain (