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

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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: 
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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 
Breadth = x cm 
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
.