Class 6 Mathematics Sindh Textbook Exercise Unit 3.3 Solved Notes

Exercise 3.3 Solved

Question 1

Write in index notation

(i)

2 × 2 × 2 × 3 × 5 × 3

= 2³ × 3² × 5

(ii)

3 × 5 × 5 × 5 × 7 × 7

= 3 × 5³ × 7²

(iii)

2 × 3 × 3 × 7 × 7 × 3 × 3

= 2 × 3⁴ × 7²

Question 2

Prime factorization and index notation

(i) 24

24 = 2 × 2 × 2 × 3

= 2³ × 3

(ii) 48

48 = 2 × 2 × 2 × 2 × 3

= 2⁴ × 3

(iii) 216

216 = 2 × 2 × 2 × 3 × 3 × 3

= 2³ × 3³

(iv) 250

250 = 2 × 5 × 5 × 5

= 2 × 5³

(v) 468

468 = 2 × 2 × 3 × 3 × 13

= 2² × 3² × 13

(vi) 540

540 = 2 × 2 × 3 × 3 × 3 × 5

= 2² × 3³ × 5

(vii) 1024

1024 = 2¹⁰

(viii) 5000

5000 = 2³ × 5⁴

Question 3

Can you write factorization of a prime number in index notation?

Yes. Since a prime number has only one prime factor (itself), it can be written as:

p¹

Example:

7 = 7¹

13 = 13¹

17 = 17¹

Conclusion

This chapter helps students understand factors, multiples, divisibility rules, prime numbers, composite numbers, and prime factorization. Mastering these concepts builds a strong foundation for higher mathematics and algebra.