Question

Determinati ultima cifra a numerelor...​

Answer 1

Explicație pas cu pas:

b)

$u( {99}^{51} ) = u( {9}^{51} ) = u( {9}^{2 \cdot 25} \cdot 9) = \\ = u( {9}^{2})\cdot u(9) = 1 \cdot 9 = \red {\bf 9}$

c) 11⁵³ + 15⁵³ + 17⁵³

$u( {11}^{53}) = u( {1}^{53}) = u(1) = 1$

$u({15}^{53}) = u({5}^{53}) = u(5) = 5$

$u({17}^{53}) = u({7}^{53}) = u({7}^{4 \cdot 13} \cdot 7) = \\ = u({7}^{4}) \cdot u(7) = 1 \cdot 7 = 7$

=>

$u( {11}^{53} + {15}^{53} + {17}^{53}) = u(1 + 5 + 7) = \\ = u(13) = \red{\bf 3}$

d)

$u({313}^{100}) = u({3}^{100}) = u({3}^{4 \cdot 25}) = u( {3}^{4} ) = \red {\bf 1}$

e)

$u({68}^{86}) = u({8}^{86}) = u({8}^{4 \cdot 21} \cdot {8}^{2} ) = u( {8}^{4} ) \cdot u({8}^{2}) = \\ = u(6 \cdot 4) = u(24) = \red {\bf 4}$

f) 89³⁷ + 88³⁸ + 87³⁹

$u( {89}^{37}) = u( {9}^{37}) = u( {9}^{2 \cdot 18} \cdot 9) = \\ = u( {9}^{2})\cdot u(9) = 1 \cdot 9 = 9$

$u( {88}^{38}) = u( {8}^{38}) = u({8}^{4 \cdot 9} \cdot {8}^{2} ) = u( {8}^{4} ) \cdot u({8}^{2}) = \\ = u(6 \cdot 4) = u(24) = 4$

$u( {87}^{39}) = u( {7}^{39}) = u({7}^{4 \cdot 9} \cdot {7}^{3} ) = \\ = u({7}^{4}) \cdot u( {7}^{3} ) = 1 \cdot 3 = 3$

=>

$u( {89}^{37}) + u( {88}^{38}) + u( {87}^{39}) = u(9 + 4 + 3) = u(16) = \red {\bf 6}$