Explicație pas cu pas:
16.a)
[tex]( - 2)^{6} = {2}^{6} > - {2}^{6} [/tex]
b)
[tex]{( - 3)}^{3} = - {3}^{3} [/tex]
c)
[tex]{( - 4)}^{0} = 1[/tex]
[tex]- {4}^{0} = - 1[/tex]
[tex]\implies {( - 4)}^{0} > - {4}^{0}[/tex]
d)
[tex]{( - {5}^{3} )}^{2} = {({5}^{3} )}^{2} = {5}^{6}[/tex]
[tex] - {({5}^{3} )}^{2} = - {5}^{6}[/tex]
[tex]\implies {( - {5}^{3} )}^{2} > \implies - {({5}^{3} )}^{2} [/tex]
e)
[tex]{( - {6}^{4} )}^{7} = - {6}^{28} [/tex]
[tex]- {36}^{14} = - {({6}^{2} )}^{14} = - {6}^{28} \\ [/tex]
[tex]\implies {( - {6}^{4} )}^{7} = - {36}^{14} [/tex]
f)
[tex]{( - 8)}^{24} = {8}^{24} [/tex]
[tex]{( - 64)}^{12} = {( - {8}^{2} )}^{12} = {8}^{24} \\ [/tex]
[tex]\implies {( - 8)}^{24} = {( - 64)}^{12}[/tex]
17. 987
a) 987 + (-99) = 888
b) 987 + (-987) = 0
c) 987 + (-9876) = -8889
18.
a) -5 < x < 14, x ∈ Z
=> x ∈ {-4, -3, ..., 12, 13}
[tex]S = ( - 4) + ( - 3) + ... + 0 + 1 + 2+ ... + 13 \\ = - (4 + 3 + 2 + 1) + 0 + 1 + 2 + ... + 13 \\ = \frac{13 \times 14}{2} - \frac{4 \times 5}{2} = \frac{182 - 20}{2} = \frac{162}{2} = 81[/tex]
b) |x| < 20, x ∈ Z => -20 < x < 20
=> x ∈ {-19, -18, ..., 18, 19}
[tex]S = ( - 19) + ( - 18) + ... + ( - 1) + 0 + 1 + ... + 18 + 19 \\ = - (19 + 18 + ... + 2 + 1) + 0 + (1 + 2 + ... + 18 + 19) \\ = \frac{19 \times 20}{2} - \frac{19 \times 20}{2} = 0[/tex]
19.
- 8° - 3° = - 12°
