Question

aflati ultima cifra a numerelor :   a=4la puterea75 +5 la puterea 2003 +6 la puterea 2001 si           b=2 la puterea1001- 3la puterea 99 +7 la puterea 186 -9 la puterea 43

Answer 1

a=4⁷⁵ +5 ²°°³ +6 ²°°¹4¹=4
4²=16
4³=64⇒se repeta din doi in doi ultima cifra⇒75:2=37 rest 1⇒4¹ are ultima cifra 4 deci 4⁷⁵ are ultima cifra 4

5 la orice putere are ultima cifra 5 5²°°³ are ulrima cifra 5
6 la orice putere are ultima cifra 6 6²°°¹ are ulrima cifra 6

a=.....4+...5+....6=....15    5 este ultima cifra a lui a

b=2 ¹°°¹- 3⁹⁹ +7 ¹⁸⁶ -9⁴³

2¹=2
2²=4
2³=8
2⁴=16
2⁵=32⇒se repeta din4 in 4⇒1001:4=250 rest 1 ,deci 2¹=2 rezulta 2¹°°¹=....2

3¹=3
3²=9
3³=27
3⁴=81
3⁵=243⇒se repeta din4 in 4⇒99:4=24 rest 3, 3³=27 rezulta 3⁹⁹=......7

7¹=7
7²=49
7³=343
7⁴=2401⇒se repeta din4 in 4⇒186:4=46 rest  2 ,7²=49 rezulta 7¹⁸⁶=......9

9¹=9
9²=81 ⇒se repeta din2 in 2⇒43:2=21 rest 1  , 9¹=9 rezulta 9⁴³=......9

b=2 ¹°°¹- 3⁹⁹ +7 ¹⁸⁶ -9⁴³=..2-..7+..9-..9=...5