Ex-8.2, Introduction To Algebra, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

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) a¹⁵

(ii) 8a⁴b³

(iii) 5a³b²c³

(iv) 7a⁸b⁵

(v) 4a⁵b¹²c¹⁵

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

(i) a²b⁵ (ii) 8x³

(iii) 7a³b⁴ (iv) 15a⁹b⁸c⁶

(v) 30x⁴y⁴z⁵ (vi) 43p¹⁰q⁵r¹⁵

(vii) 17p¹²q²⁰

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) 4a³×6ab²×c²

(ii) 5xy×3x²y×7y²

(iii) a³×3ab²×2a²b²

Solution:

(i) 24a⁴b²c²

(ii) 105x³y⁴

(iii) 6a⁶b⁴

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 = x²

Number of bacteria in the culture after two weeks = (x²)²=x⁴

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 = 23cm²

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×x²=x³