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