# RD Sharma Solutions Class 6 Introduction To Algebra Exercise 8.2

## RD Sharma Solutions Class 6 Chapter 8 Exercise 8.2

#### Exercise 8.2

Question 1. Write each of the following products inb 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 × a X. . . . 5 times × b × b × . . . 12 times × c × c × c . . . 15 times

Solution:

(i) $a^{15}$

(ii) $8 a^{4} b^{3}$

(iii) $5 a^{3} b^{2} c^{3}$

(iv) $7 a^{ 8 } b^{5}$

(v) $4 a^{ 5 } b^{ 12 } c^{ 15 }$

2. Write each of the following in the product form:

(i) $a^{ 2 } b^{ 5 }$ (ii) $8 x^{ 3 }$

(iii) $7 a^{ 3 } b^{ 4 }$ (iv) $15 a^{ 9 } b^{ 8 } c^{6}$

(v) $30 x^{ 4 } y^{ 4 } z^{5}$ (vi) $43 p^{10} q^{5} r^{15}$

(vii) $17p^{12 } q^{ 20 }$

Solution:

(i) a × a × b × b × b × b × b

(ii) 8 × x × x × x

(iii) 7 × a × a × a × b × b × b × b

(iv) 15 × a × a × a ×. . . 9 times × b × b × b × . . . 8 times

(v) 30 ×

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

(i) $4 a ^{3} \times 6 ab^{2} \times c^{2}$

(ii) $5 xy \times 3x^{2}y \times 7y^{2}$

(iii) $a^{ 3 } \times 3a b ^{ 2 } \times 2 a^{ 2 } b^{ 2 }$

Solution:

(i) $24 a^{4} b^{2} c^{2}$

(ii) $105 x^{3} y^{4}$

(iii) $6 a ^{6} b^{4}$

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:

Present number of bacteria in a culture = x

Number of bacteria in the culture after one week = $x^{2}$

Number of bacteria in the culture after two weeks = $\left (x^{2} \right ) ^{2} = x^{4}$

5. The area of a rectangle is given by the product of its length and breadth. The length of a reactangle is two-thirs of its breadth. Find its area if its breadth is x cm.

Solution:

Breadth of the given rectangle = x cm

Length of the rectangle = 23 x cm

Area of the rectangle = 23x × x = $23 cm^{2}$

6. If there are x rows of chairs and each row contains x2 chairs. Determine the total numbers of chairs.

Solution:

Total number of chairs = Number of rows × Number of chairs in each row

= $x \times x^{2} = x^{3}$