Question

Find the unit digit of expanded form.

(i) 25²³

(ii) 11¹⁰

(iii) 46¹⁵

(iv) 100¹²

(v) 29²¹

(vi) 19¹²

(vii) 24²⁵

(viii) 34¹⁶

Answer 1

(i) 25²³

Unit digit of base 25 is 5 and power is 23. Thus the unit digit of 25²³ is 5.

(ii) 11¹⁰

Unit digit of base 11 is 1 and power is 10. Thus the unit digit of 11¹⁰ is 1.

(iii) 46¹⁵

Unit digit of base 46 is 6 and power is 15. Thus the unit digit of 46¹⁵ is 6.

(iv) 100¹²

Unit digit of base 100 is 0 and power is 12. Thus the unit digit of 100¹² is 0.

(v) 29²¹

Unit digit of base 29 is 9 and power is 21 (odd power).

Therefore, unit digit of 29²¹ is 9.

(vi) 19¹²

Unit digit of base 19 is 9 and power is 12 (even power).

Therefore, unit digit of 19¹² is 1.

(vii) 24²⁵

Unit digit of base 24 is 4 and power is 25 (odd power).

Therefore, unit digit of 24²⁵ is 4.

(viii) 34¹⁶

Unit digit of base 34 is 4 and power is 16 (even power).

Therefore, unit digit of 34¹⁶ is 6.