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) \( a^{ 2 } b^{ 5 }\)
(iii) \(7 a^{ 3 } b^{ 4 }\)
(v) \(30 x^{ 4 } y^{ 4 } z^{5}\)
(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
= \(x \times x^{2} = x^{3}\)
