Page 1 Exercise 8.2 page: 8.11 1. Write each of the following products in exponential form: (i) a × a × a × a × …….. 15 times (ii) 8 × b × b × b × a × a × a × a (iii) 5 × a × a × a × b × b × c × c × c (iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times (v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 15 times Solution: (i) a × a × a × a × …….. 15 times is written in exponential form as a 15 . (ii) 8 × b × b × b × a × a × a × a is written in exponential form as 8a 4 b 3 . (iii) 5 × a × a × a × b × b × c × c × c is written in exponential form as 5a 3 b 2 c 3 . (iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times is written in exponential form as 7a 8 b 5 . (v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 15 times is written in exponential form as 4a 5 b 12 c 15 . 2. Write each of the following in the product form: (i) a 2 b 5 (ii) 8x 3 (iii) 7a 3 b 4 (iv) 15 a 9 b 8 c 6 (v) 30x 4 y 4 z 5 (vi) 43p 10 q 5 r 15 (vii) 17p 12 q 20 Solution: (i) a 2 b 5 is written in the product form as a × a × b × b × b × b × b. (ii) 8x 3 is written in the product form as 8 × x × x × x. (iii) 7a 3 b 4 is written in the product form as 7 × a × a × a × b × b × b × b. (iv) 15 a 9 b 8 c 6 is written in the product form as 15 × a × a …… 9 times × b × b × … 8 times × c × c × ….. 6 times. (v) 30x 4 y 4 z 5 is written in the product form as 30 × x × x × x × x × y × y × y × y × z × z × z × z × z. (vi) 43p 10 q 5 r 15 is written in the product form as 43 × p × p …. 10 times × q × q …. 5 times × r × r × …. 15 times. (vii) 17p 12 q 20 is written in the product form as 17 × p × p …. 12 times × q × q × ….. 20 times. 3. Write down each of the following in exponential form: (i) 4a 3 × 6ab 2 × c 2 (ii) 5xy × 3x 2 y × 7y 2 (iii) a 3 × 3ab 2 × 2a 2 b 2 Solution: Page 2 Exercise 8.2 page: 8.11 1. Write each of the following products in exponential form: (i) a × a × a × a × …….. 15 times (ii) 8 × b × b × b × a × a × a × a (iii) 5 × a × a × a × b × b × c × c × c (iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times (v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 15 times Solution: (i) a × a × a × a × …….. 15 times is written in exponential form as a 15 . (ii) 8 × b × b × b × a × a × a × a is written in exponential form as 8a 4 b 3 . (iii) 5 × a × a × a × b × b × c × c × c is written in exponential form as 5a 3 b 2 c 3 . (iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times is written in exponential form as 7a 8 b 5 . (v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 15 times is written in exponential form as 4a 5 b 12 c 15 . 2. Write each of the following in the product form: (i) a 2 b 5 (ii) 8x 3 (iii) 7a 3 b 4 (iv) 15 a 9 b 8 c 6 (v) 30x 4 y 4 z 5 (vi) 43p 10 q 5 r 15 (vii) 17p 12 q 20 Solution: (i) a 2 b 5 is written in the product form as a × a × b × b × b × b × b. (ii) 8x 3 is written in the product form as 8 × x × x × x. (iii) 7a 3 b 4 is written in the product form as 7 × a × a × a × b × b × b × b. (iv) 15 a 9 b 8 c 6 is written in the product form as 15 × a × a …… 9 times × b × b × … 8 times × c × c × ….. 6 times. (v) 30x 4 y 4 z 5 is written in the product form as 30 × x × x × x × x × y × y × y × y × z × z × z × z × z. (vi) 43p 10 q 5 r 15 is written in the product form as 43 × p × p …. 10 times × q × q …. 5 times × r × r × …. 15 times. (vii) 17p 12 q 20 is written in the product form as 17 × p × p …. 12 times × q × q × ….. 20 times. 3. Write down each of the following in exponential form: (i) 4a 3 × 6ab 2 × c 2 (ii) 5xy × 3x 2 y × 7y 2 (iii) a 3 × 3ab 2 × 2a 2 b 2 Solution: (i) 4a 3 × 6ab 2 × c 2 is written in exponential form as 24a 4 b 2 c 2 . (ii) 5xy × 3x 2 y × 7y 2 is written in exponential form as 105x 3 y 4 . (iii) a 3 × 3ab 2 × 2a 2 b 2 is written in exponential form as 6a 6 b 4 . 4. The number of bacteria in a culture is x now. It becomes square of itself after one week. What will be its number after two weeks? Solution: Number of bacteria in a culture = x It is given that Number of bacteria becomes square of itself in one week = x 2 So the number of bacteria after two weeks = (x 2 ) 2 = x 4 Hence, the number of bacteria after two weeks is x 4 . 5. The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two- third of its breadth. Find its area if its breadth is x cm. Solution: It is given that Area of rectangle = l × b Breadth = x cm Length = (2/3) x cm So the area of the rectangle = (2/3) x × x = (2/3) x 2 cm 2 Hence, the area of rectangle is (2/3) x 2 cm 2 . 6. If there are x rows of chairs and each row contains x 2 chairs. Determine the total number of chairs. Solution: Number of rows of chairs = x Each row contains = x 2 chairs So the total number of chairs = number of rows of chairs × chairs in each row We get Total number of chairs = x × x 2 = x 3 Hence, the total number of chairs is x 3 .Read More

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