RD Sharma Solutions: Introduction to Algebra (Exercise 8.2)

# Introduction to Algebra (Exercise 8.2) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

``` Page 1

Exercise 8.2                                                                               page: 8.11
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 a
15
.

(ii) 8 × b × b × b × a × a × a × a is written in exponential form as 8a
4
b
3
.

(iii) 5 × a × a × a × b × b × c × c × c is written in exponential form as 5a
3
b
2
c
3
.

(iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times is written in exponential form as 7a
8
b
5
.

(v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 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 × a × b × b × b × b × b.

(ii) 8x
3
is written in the product form as 8 × x × x × x.

(iii) 7a
3
b
4
is written in the product form as 7 × a × a × a × b × b × b × b.

(iv) 15 a
9
b
8
c
6
is written in the product form as 15 × a × a …… 9 times × b × b × … 8 times × c × c × ….. 6 times.

(v) 30x
4
y
4
z
5
is written in the product form as 30 × x × x × x × x × y × y × y × y × z × z × z × z × z.

(vi) 43p
10
q
5
r
15
is written in the product form as 43 × p × p …. 10 times × q × q …. 5 times × r × r × …. 15 times.

(vii) 17p
12
q
20
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) 4a
3
× 6ab
2
× c
2

(ii) 5xy × 3x
2
y × 7y
2

(iii) a
3
× 3ab
2
× 2a
2
b
2

Solution:
Page 2

Exercise 8.2                                                                               page: 8.11
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 a
15
.

(ii) 8 × b × b × b × a × a × a × a is written in exponential form as 8a
4
b
3
.

(iii) 5 × a × a × a × b × b × c × c × c is written in exponential form as 5a
3
b
2
c
3
.

(iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times is written in exponential form as 7a
8
b
5
.

(v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 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 × a × b × b × b × b × b.

(ii) 8x
3
is written in the product form as 8 × x × x × x.

(iii) 7a
3
b
4
is written in the product form as 7 × a × a × a × b × b × b × b.

(iv) 15 a
9
b
8
c
6
is written in the product form as 15 × a × a …… 9 times × b × b × … 8 times × c × c × ….. 6 times.

(v) 30x
4
y
4
z
5
is written in the product form as 30 × x × x × x × x × y × y × y × y × z × z × z × z × z.

(vi) 43p
10
q
5
r
15
is written in the product form as 43 × p × p …. 10 times × q × q …. 5 times × r × r × …. 15 times.

(vii) 17p
12
q
20
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) 4a
3
× 6ab
2
× c
2

(ii) 5xy × 3x
2
y × 7y
2

(iii) a
3
× 3ab
2
× 2a
2
b
2

Solution:

(i) 4a
3
× 6ab
2
× c
2
is written in exponential form as 24a
4
b
2
c
2
.
(ii) 5xy × 3x
2
y × 7y
2
is written in exponential form as 105x
3
y
4
.
(iii) a
3
× 3ab
2
× 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 × b
Length = (2/3) x cm
So the area of the rectangle = (2/3) x × 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 number of chairs = number of rows of chairs × chairs in each row
We get
Total number of chairs = x × x
2
= x
3

Hence, the total number of chairs is x
3
.
```

## Mathematics (Maths) Class 6

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## FAQs on Introduction to Algebra (Exercise 8.2) RD Sharma Solutions - Mathematics (Maths) Class 6

 1. What is algebra and why is it important?
Ans. Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols to solve mathematical equations. It helps us solve complex problems, make predictions, analyze patterns, and understand the relationships between variables. Algebra is important because it is used in various fields like science, engineering, economics, and computer science.
 2. How can algebra be applied in real-life situations?
Ans. Algebra can be applied in various real-life situations. For example, it can be used to calculate the cost of items on sale, determine the best route for a road trip, analyze data trends, design structures, and solve financial problems like calculating interest rates or loan payments. Algebraic concepts and equations are used in many practical scenarios to solve problems and make informed decisions.
 3. What are the basic operations in algebra?
Ans. The basic operations in algebra are addition, subtraction, multiplication, and division. These operations are used to perform calculations and manipulate algebraic expressions. Addition combines two or more terms, subtraction subtracts one term from another, multiplication multiplies terms together, and division divides one term by another. These operations follow certain rules and properties that help simplify expressions and solve equations.
 4. How can I improve my algebra skills?
Ans. To improve your algebra skills, it is important to practice regularly and understand the fundamental concepts. Start by mastering the basic operations and rules of algebra. Solve a variety of problems, both simple and complex, to develop problem-solving skills. Work on building a strong foundation in algebraic concepts like equations, inequalities, functions, and graphs. Seek help from teachers, online resources, or tutoring if needed.
 5. What are some common mistakes to avoid in algebra?
Ans. There are a few common mistakes to avoid in algebra. One is not following the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) while evaluating expressions. Another mistake is not applying the distributive property correctly. It is also important to pay attention to signs and not overlook negative signs or ignore signs while simplifying expressions. Additionally, be cautious with algebraic fractions and avoid canceling out terms without proper simplification. Double-checking calculations can help catch errors and avoid these common mistakes in algebra.

## Mathematics (Maths) Class 6

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