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**Question 1. Write each of the following products inb exponential form:**

**(i) a Ã— a Ã— a Ã— a Ã— . . . 15 times**

**(ii) 8 Ã— b Ã— b Ã— b Ã— a Ã— a Ã— a Ã— a**

**(iii) 5 Ã— a Ã— a Ã— a Ã— b Ã— b Ã— c Ã— c Ã— c**

**(iv) 7 Ã— a Ã— a Ã— aâ€¦ 8 times Ã— b Ã— b Ã— b Ã— .. . 5 times**

**(v) 4 Ã— a Ã— a Ã— a X. . . . 5 times Ã— b Ã— b Ã— . . . 12 times Ã— c Ã— c Ã— c . . . 15 times**

**Solution:**

(i) a^{15}

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

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

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

(v) 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) 15a^{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 Ã— a Ã— b Ã— b Ã— b Ã— b Ã— b

(ii) 8 Ã— x Ã— x Ã— x

(iii) 7 Ã— a Ã— a Ã— a Ã— b Ã— b Ã— b Ã— b

(iv) 15 Ã— a Ã— a Ã— a Ã—. . . 9 times Ã— b Ã— b Ã— b Ã— . . . 8 times

(v) 30 Ã—

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

**(i) 4a ^{3}Ã—6ab^{2}Ã—c^{2}**

**(ii) 5xyÃ—3x ^{2}yÃ—7y^{2}**

**(iii) a ^{3}Ã—3ab^{2}Ã—2a^{2}b^{2}**

**Solution:**

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

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

(iii) 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: **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 = (x^{2})^{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 Ã— x = 23cm^{2}

6. If there are x rows of chairs and each row contains x^{2} chairs. Determine the total numbers of chairs.

Solution:

Total number of chairs = Number of rows Ã— Number of chairs in each row

= xÃ—x^{2}=x^{3}