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 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 Chapter 8: Introduction to Algebra Exercise 8.2 Download PDF

### Access RD Sharma Solutions for Class 6 Chapter 8: Introduction to Algebra Exercise 8.2

Exercise 8.2 page: 8.11

**1. Write each of the following products in exponential form:**

**(i) a Ã— a Ã— a Ã— a Ã— â€¦â€¦.. 15 times**

**(ii) 8 Ã— b Ã— b Ã— b Ã— a Ã— a Ã— a Ã— a**

**(iii) 5 Ã— a Ã— a Ã— a Ã— b Ã— b Ã— c Ã— c Ã— c**

**(iv) 7 Ã— a Ã— a Ã— a â€¦â€¦.. 8 times Ã— b Ã— b Ã— b Ã— â€¦â€¦ 5 times**

**(v) 4 Ã— a Ã— a Ã— â€¦â€¦ 5 times Ã— b Ã— b Ã— â€¦â€¦. 12 times Ã— c Ã— c â€¦â€¦ 15 times**

**Solution:**

(i) a Ã— a Ã— a Ã— a Ã— â€¦â€¦.. 15 times is written in exponential form as a^{15}.

(ii) 8 Ã— b Ã— b Ã— b Ã— a Ã— a Ã— a Ã— a is written in exponential form as 8a^{4}b^{3}.

(iii) 5 Ã— a Ã— a Ã— a Ã— b Ã— b Ã— c Ã— c Ã— c is written in exponential form as 5a^{3}b^{2}c^{3}.

(iv) 7 Ã— a Ã— a Ã— a â€¦â€¦.. 8 times Ã— b Ã— b Ã— b Ã— â€¦â€¦ 5 times is written in exponential form as 7a^{8}b^{5}.

(v) 4 Ã— a Ã— a Ã— â€¦â€¦ 5 times Ã— b Ã— b Ã— â€¦â€¦. 12 times Ã— c Ã— c â€¦â€¦ 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 Ã— a Ã— b Ã— b Ã— b Ã— b Ã— b.

(ii) 8x^{3} is written in the product form as 8 Ã— x Ã— x Ã— x.

(iii) 7a^{3}b^{4} is written in the product form as 7 Ã— a Ã— a Ã— a Ã— b Ã— b Ã— b Ã— b.

(iv) 15 a^{9}b^{8}c^{6} is written in the product form as 15 Ã— a Ã— a â€¦â€¦ 9 times Ã— b Ã— b Ã— â€¦ 8 times Ã— c Ã— c Ã— â€¦.. 6 times.

(v) 30x^{4}y^{4}z^{5} is written in the product form as 30 Ã— x Ã— x Ã— x Ã— x Ã— y Ã— y Ã— y Ã— y Ã— z Ã— z Ã— z Ã— z Ã— z.

(vi) 43p^{10}q^{5}r^{15} is written in the product form as 43 Ã— p Ã— p â€¦. 10 times Ã— q Ã— q â€¦. 5 times Ã— r Ã— r Ã— â€¦. 15 times.

(vii) 17p^{12}q^{20} is written in the product form as 17 Ã— p Ã— p â€¦. 12 times Ã— q Ã— q Ã— â€¦.. 20 times.

**3. Write down each of the following in exponential form:**

**(i) 4a ^{3 }Ã— 6ab^{2} Ã— c^{2}**

**(ii) 5xy Ã— 3x ^{2}y Ã— 7y^{2}**

**(iii) a ^{3} Ã— 3ab^{2} Ã— 2a^{2}b^{2}**

**Solution:**

(i) 4a^{3 }Ã— 6ab^{2} Ã— c^{2} is written in exponential form as 24a^{4}b^{2}c^{2}.

(ii) 5xy Ã— 3x^{2}y Ã— 7y^{2} is written in exponential form as 105x^{3}y^{4}.

(iii) a^{3} Ã— 3ab^{2} Ã— 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 Ã— b

Breadth = x cm

Length = 2/3 x cm

So the area of the rectangle = 2/3 x Ã— 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 numbers of chairs = number of rows of chairs Ã— chairs in each row

We get

Total number of chairs = x Ã— x^{2} = x^{3}

Hence, the total number of chairs is x^{3}.