Grade 8 Exponents and Powers - PDF Free Download

ID : ae-8-exponents-and-powers [] Grade 8 Exponents and Powers For more such worksheets visit www.edugain.com 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) 0.00000082 C) 0.0075 D) 0.000046 (3) 4.4 0-3. 0 26? (4) If, and, f ind the value of xyz. (5) Write f ollowing numbers in usual f orm A) 7.6 0-4 B) 2.2 0-6 C).4 0 7 D).9 0 7 (6) If 4 x 4 + 4 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. -28 9 b. 52 432 c. -64 432 d. -28 432 (9) What is the unit's digit in (267) 3 X (267) 00? a. b. 9 c. 3 d. 7 (C) 206 Edugain (www.edugain.com)

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 3 975 2 974? a. 9 49 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. 4096-4096 b. -4096 d. 4096 (4) Simplif y (243) -3/5 3? a. - b. c. 9 d. - 9 (5) Simplif y. a. b. c. d. (C) 206 Edugain (www.edugain.com)

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) 6.5 0 7 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 6.5 0 7 B) 8.2 0-7 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 8.2 0-7 (C) 206 Edugain (www.edugain.com)

C) 7.5 0-3 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 7.5 0-3 D) 4.6 0-5 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 4.6 0-5 (3) 4.09 0 Step We have been asked to f ind the value of 4.4 0-3. 0 26. 4.4 0-3. 0 26 4.4 0-0.3 0 0 26 4.4 0-0.3 0 (4.4-0.3) 0 4.09 0 Theref ore, the value of 4.4 0-3. 0 26 is 4.09 0. (C) 206 Edugain (www.edugain.com)

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 (www.edugain.com)

(5) A) 0.00076 ID : ae-8-exponents-and-powers [7] Step We have been asked to f ind the usual f orm of the number 7.6 0-4. 7.6 0-4 76 0.00076 00000 Theref ore, the usual f orm of 7.6 0-4 is 0.00076. B) 0.0000022 Step We have been asked to f ind the usual f orm of the number 2.2 0-6. 2.2 0-6 22 0.0000022 0000000 Theref ore, the usual f orm of 2.2 0-6 is 0.0000022. C) 4,000,000 Step We have been asked to f ind the usual f orm of the number.4 0 7..4 0 7 4 000000 4,000,000 Theref ore, the usual f orm of.4 0 7 is 4,000,000. (C) 206 Edugain (www.edugain.com)

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.9 0 7..9 0 7 9 000000 9,000,000 Theref ore, the usual f orm of.9 0 7 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 3 3 3 3) 3/5 3 5 (3/5) 3 3 Theref ore, the value of 243 3/5 is. (C) 206 Edugain (www.edugain.com)

(8) a. -28 9 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 ) 2 64-8 -28 9 6 9 Theref ore, the value of is -28 9. (C) 206 Edugain (www.edugain.com)

(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 (www.edugain.com)

(0) d. 6 Step We have been asked to f ind the value of 32-4/5. 32-4/5 32 4/5 ID : ae-8-exponents-and-powers [] (2 2 2 2 2) 4/5 2 5 4/5 2 4 6 Theref ore, the value of 32-4/5 is 6. (C) 206 Edugain (www.edugain.com)

() 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, 7 973 x 3 975 2 974 7 973 3 975 (7 3) 974 7973 3 975 7 974 3 974 [since (xy) n x n y n ] 3 975 3-974 7 974 7-973 3(975-974) 7 (974-973) 3 7 3 7 Theref ore, the value of 7973 x 3 975 2 974 is 3 7. (C) 206 Edugain (www.edugain.com)

(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 ( 3 3 3 ) ((-4) (-4) ) ( ) (6) 6 Thus, the value of 3-3 (-4) 2 is 6. (C) 206 Edugain (www.edugain.com)

(3) a. 4096 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 4096. (4) c. 9 Step Lets f irst f ind prime f actors of 243, 243 3 3 3 3 3 (243) -3/5 3 (3 3 3 3 3) -3/5 3 (3 5 ) -3/5 3 (3) -3 3 3 (3) 3 9 (C) 206 Edugain (www.edugain.com)

(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 6-5 6 + 5 6-5 6 + 5 6 + 5 ( 6 + 5) 2 ( 6) 2 - ( 5) 2 ( 6)2 + ( 5) 2 + 2 6 5 6-5 6 + 5 + 2 30 + 2 30 Theref ore, the simplif ication of 6 + 5 6-5 is + 2 30. (C) 206 Edugain (www.edugain.com)