The students who aspire to perform well in the exam can solve problems using RD Sharma Solutions Class 6. The solutions consist of explanations in a simple language which matches the understanding ability of students. The problems of RD Sharma textbook can be solved by using the solutions as a reference guide. With the help of RD Sharma Solutions for Class 6 Maths Chapter 8 Introduction to Algebra Exercise 8.2 PDF students can expertise the concepts which are important for the exam preparation.
RD Sharma Solutions for Class 6 Maths Chapter 8: Introduction to Algebra Exercise 8.2 Download PDF
Access answers to Maths RD Sharma Solutions for Class 6 Chapter 8: Introduction to Algebra Exercise 8.2
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 a15.
(ii) 8 × b × b × b × a × a × a × a is written in exponential form as 8a4b3.
(iii) 5 × a × a × a × b × b × c × c × c is written in exponential form as 5a3b2c3.
(iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times is written in exponential form as 7a8b5.
(v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 15 times is written in exponential form as 4a5b12c15.
2. Write each of the following in the product form:
(i) a2 b5
(ii) 8x3
(iii) 7a3b4
(iv) 15 a9b8c6
(v) 30x4y4z5
(vi) 43p10q5r15
(vii) 17p12q20
Solution:
(i) a2 b5 is written in the product form as a × a × b × b × b × b × b.
(ii) 8x3 is written in the product form as 8 × x × x × x.
(iii) 7a3b4 is written in the product form as 7 × a × a × a × b × b × b × b.
(iv) 15 a9b8c6 is written in the product form as 15 × a × a …… 9 times × b × b × … 8 times × c × c × ….. 6 times.
(v) 30x4y4z5 is written in the product form as 30 × x × x × x × x × y × y × y × y × z × z × z × z × z.
(vi) 43p10q5r15 is written in the product form as 43 × p × p …. 10 times × q × q …. 5 times × r × r × …. 15 times.
(vii) 17p12q20 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) 4a3 × 6ab2 × c2
(ii) 5xy × 3x2y × 7y2
(iii) a3 × 3ab2 × 2a2b2
Solution:
(i) 4a3 × 6ab2 × c2 is written in exponential form as 24a4b2c2.
(ii) 5xy × 3x2y × 7y2 is written in exponential form as 105x3y4.
(iii) a3 × 3ab2 × 2a2b2 is written in exponential form as 6a6b4.
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 = x2
So the number of bacteria after two weeks = (x2)2 = x4
Hence, the number of bacteria after two weeks is x4.
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 x2 cm2
Hence, the area of rectangle is (2/3) x2 cm2.
6. If there are x rows of chairs and each row contains x2 chairs. Determine the total number of chairs.
Solution:
Number of rows of chairs = x
Each row contains = x2 chairs
So the total number of chairs = number of rows of chairs × chairs in each row
We get
Total number of chairs = x × x2 = x3
Hence, the total number of chairs is x3.
