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Chapter 8: Introduction to Algebra – Exercise 8.2 Question: 1 Write each of the following products into 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 × a ×. . . . 5 times × b × b × . . . 12 times × c × c × c . . . 15 times Solution: (i) a15 (ii) 8a4b3 (iii) 5a3b2c3 (iv) 7a8b5 (v) 4a5b12c15 Question: 2 Write each of the following in the product form: (i) a2b5 (ii) 8x3 (iii) 7a3b4 (iv) 15a9b8c6 (v) 30x4y4z5 (vi) 43p10q5r15 (vii) 17p12q20 Solution: (i) a × a × b × b × b × b × b (ii) 8 × x × x × x (iii) 7 × a × a × a × b × b × b × b (iv) 15 × a × a × a ×. . . 9 times × b × b × b × . . . 8 times (v) 30 × x × x × x × x y × y × y × y × z × z … 5 times (vi) 43 × p × p ….. 10 times × q × q … 5 times × r × r ….. 15 times (vii) 17 × p × p … 12 times × q × q … 20 times Question: 3 Write down each of the following in the exponential form: (i) 4a3 × 6ab2 × c2 (ii) 5xy × 3x2y × 7y2 (iii) a3 × 3ab2 × 2a2b2 Solution: (i) 24a4b2c2 (ii) 105x3y4 (iii) 6a6b4 Question: 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: Present number of bacteria in a culture = x Number of bacteria in the culture after one week = x2 Number of bacteria in the culture after two weeks = (x2)2 = x4 Question: 5 The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two-thirs of its breadth. Find its area if its breadth is x cm. Solution: Breadth of the given rectangle = x cm Length of the rectangle = 23 x cm Area of the rectangle = 23x × x = 23 cm2 Question: 6 If there are x rows of chairs and each row contains x2 chairs. Determine the total numbers of chairs. Solution: Total number of chairs = Number of rows × Number of chairs in each row = x × x2 = x3
Write each of the following products into 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 × a ×. . . . 5 times × b × b × . . . 12 times × c × c × c . . . 15 times
(i) a15
(ii) 8a4b3
(iii) 5a3b2c3
(iv) 7a8b5
(v) 4a5b12c15
Write each of the following in the product form:
(i) a2b5
(ii) 8x3
(iii) 7a3b4
(iv) 15a9b8c6
(v) 30x4y4z5
(vi) 43p10q5r15
(vii) 17p12q20
(i) a × a × b × b × b × b × b
(ii) 8 × x × x × x
(iii) 7 × a × a × a × b × b × b × b
(iv) 15 × a × a × a ×. . . 9 times × b × b × b × . . . 8 times
(v) 30 × x × x × x × x y × y × y × y × z × z … 5 times
(vi) 43 × p × p ….. 10 times × q × q … 5 times × r × r ….. 15 times
(vii) 17 × p × p … 12 times × q × q … 20 times
Write down each of the following in the exponential form:
(i) 4a3 × 6ab2 × c2
(ii) 5xy × 3x2y × 7y2
(iii) a3 × 3ab2 × 2a2b2
(i) 24a4b2c2
(ii) 105x3y4
(iii) 6a6b4
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?
Present number of bacteria in a culture = x
Number of bacteria in the culture after one week = x2
Number of bacteria in the culture after two weeks = (x2)2 = x4
The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two-thirs of its breadth. Find its area if its breadth is x cm.
Breadth of the given rectangle = x cm
Length of the rectangle = 23 x cm
Area of the rectangle = 23x × x = 23 cm2
If there are x rows of chairs and each row contains x2 chairs. Determine the total numbers of chairs.
Total number of chairs = Number of rows × Number of chairs in each row
= x × x2 = x3
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Chapter 8: Introduction to Algebra –...
