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# Introduction to Algebra - Exercise 8.2 Class 6 Notes | EduRev

## Class 6 : Introduction to Algebra - Exercise 8.2 Class 6 Notes | EduRev

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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:
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
.
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## Mathematics (Maths) Class 6

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