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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
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