Grade 8 Exponents and Powers

Transcription

1 ID : ae-8-exponents-and-powers [] Grade 8 Exponents and Powers For more such worksheets visit wwwedugaincom Answer the questions ()? (2) Simplify (a -2 + b -2 ) - (3) Simplify 32-3/5 (4) Find value of following A) -3 (-2) -3 B) (-3) C) D) (-4) (5) Simplify 243 4/5 (6)? (7) Simplify (8) ? (9) What is the value of x ? (0) Simplify (243) -3/5 9 () Simplify (2) Given the following equations: 6 (a+b) 7776, and 7776 (a-b) 6, what is the value of b? (3) Find the value of the following A) (-6) -3 B) 5-5 C) 0-3 D) 5-2 (4) ( ) (4 0 3 )? (5) If, and, find the value of xyz Copyright 207 wwwedugaincom

2 ID : ae-8-exponents-and-powers [2] 207 Edugain (wwwedugaincom) All Rights Reserved Many more such worksheets can be generated at wwwedugaincom Copyright 207 wwwedugaincom

3 Answers ID : ae-8-exponents-and-powers [3] () Step Using algebraic identities (a + b) 2 a 2 + b 2 + 2ab and (a - b) 2 a 2 + b 2-2ab, [( 3) 2 + ( 7) ] - [( 3) 2 + ( 7) ] Now common terms in subtraction will cancel as following, [( 3) 2 + ( 7) ] - [( 3) 2 + ( 7) ] (2 2) - (- 2 2) 4 2 Therefore, the value of is Copyright 207 wwwedugaincom

4 ID : ae-8-exponents-and-powers [4] (2) a 2 b 2 a 2 + b 2 Step We have been asked to simplify (a -2 + b -2 ) - (a -2 + b -2 ) - a -2 + b -2 + a 2 b 2 + a 2 a 2 b 2 a 2 b 2 a 2 + b 2 b 2 Therefore, the result is a 2 b 2 a 2 + b 2 Copyright 207 wwwedugaincom

5 ID : ae-8-exponents-and-powers [5] (3) 8 Step We have been asked to find the value of 32-3/5 32-3/5 32 3/5 ( ) 3/ / Therefore, the value of 32-3/5 is 8 Copyright 207 wwwedugaincom

6 ID : ae-8-exponents-and-powers [6] (4) A) - 8 Step We have been asked to find the value of -3 (-2) -3-3 (-2) -3 3 (-2) 3 (-2) (-2) (-2) - 8 Therefore, the value of -3 (-2) -3 is - 8 B) 8 Step We have been asked to find the value of (-3) (-3) (-3) (-3) (-3) Therefore, the value of (-3) is 8 Copyright 207 wwwedugaincom

7 ID : ae-8-exponents-and-powers [7] C) 243 Step We have been asked to find the value of Therefore, the value of is 243 D) 432 Step We have been asked to find the value of (-4) (-4) (-4) (-4) (-4) Therefore, the value of (-4) is 432 Copyright 207 wwwedugaincom

8 (5) 8 ID : ae-8-exponents-and-powers [8] Step We have been asked to find the value of 243 4/5 Given, x 243 4/5 ( ) 4/5 3 5 (4/5) Therefore, the value of 243 4/5 is 8 (6) 2 3 Step Let's begin with inverting the fractions with negative powers: (-3) (-3) (2) (2) (2) (2) (2) (3) (3) (3) 2 3 Copyright 207 wwwedugaincom

9 (7) ID : ae-8-exponents-and-powers [9] On multiplying numerator and denominator by ( 2 - ), ( 2 - )( 2 -) [using a 2 - b 2 (a + b)(a - b) in denominator ] ( 2) 2 - () 2 ( 2 - )2 2 - ( 2)2 + () [using (a - b) 2 a 2 + b 2-2ab in numerator] (8) Step We have been asked to find the value of ( ) ( ) Therefore, the value of is Copyright 207 wwwedugaincom

10 ID : ae-8-exponents-and-powers [0] (9) 5 7 Step We can see that base of denominator (ie 35) is equal to products of bases of numerator (ie 7 and 5) Therefore if we write 35 as multiplication of 7 and 5 in denominator, some part will cancel out and we should be able to simplify it Therefore, x (7 5) [since (xy) n x n y n ] ( ) 7 ( ) Therefore, the value of x is 5 7 Copyright 207 wwwedugaincom

11 ID : ae-8-exponents-and-powers [] (0) 3 Step Lets first find prime factors of 243, (243) -3/5 9 ( ) -3/5 9 (3 5 ) -3/5 9 (3) (3) 3 3 () Step The denominator of the fraction can be simplified, if we multiply it by ( 7 + 6) Therefore, let's multiply both numerator and denominator by ( 7 + 6) ( 7 + 6) 2 ( 7) 2 - ( 6) 2 ( 7)2 + ( 6) Therefore, the simplification of is Copyright 207 wwwedugaincom

12 ID : ae-8-exponents-and-powers [2] (2) 2 5 Step We know that If we replace 7776 by 6 to the power 5, we get: 6 5(a-b) 6 6 (a+b) 6 5 From the above step we have: 5(a - b) or, 5a - 5b () a + b (2) or, 5a + 5b (3) [On multiplying by 5] Adding equation () and (3) we have: 0a 26 Or, a 3 5 Step 4 Putting this value in equation (2) we get: b 5 - a Or, b Or, b 2 5 Copyright 207 wwwedugaincom

13 ID : ae-8-exponents-and-powers [3] (3) A) - 26 Step We have been asked to find the value of (-6) -3 (-6) -3 (-6) 3 (-6) (-6) (-6) - 26 Therefore, the value of (-6) -3 is - 26 B) 325 Step We have been asked to find the value of Therefore, the value of 5-5 is 325 Copyright 207 wwwedugaincom

14 ID : ae-8-exponents-and-powers [4] C) 000 Step We have been asked to find the value of Therefore, the value of 0-3 is 000 D) 25 Step We have been asked to find the value of Therefore, the value of 5-2 is 25 Copyright 207 wwwedugaincom

15 (4) ID : ae-8-exponents-and-powers [5] Step We have been asked to find the value of ( ) (4 0 3 ) ( ) (4 0 3 ) ( 30 4 ) Therefore, the value of ( ) (4 0 3 ) is Copyright 207 wwwedugaincom

16 ID : ae-8-exponents-and-powers [6] (5) 2 Step According to the question, if a x 3 b, b y c and c z a, we have been asked to find the value of xyz a x 3 b a x (b) /3 a 3x b and b y c b y (c) /2 b 2y c and c z a c z (a) /2 c 2z a Put the value of c in c 2z a a (b 2y ) 2z a b 2 2 yz a b 4yz Now put the value of b a (a 3x ) 4yz a a 3 4 xyz a a 2xyz Step 4 On comparing powers in above equation, 2xyz xyz 2 Step 5 Therefore, the value of xyz is 2 Copyright 207 wwwedugaincom