RD Sharma Solutions Class 6 Introduction To Algebra Exercise 8.2

RD Sharma Solutions Class 6 Chapter 8 Exercise 8.2

RD Sharma Class 6 Solutions Chapter 8 Ex 8.2 PDF Free Download

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

= \(x \times x^{2} = x^{3}\)


Practise This Question

When 5 is added to a number, we get 15. How do we represent this in the form of an equation?