Question

Repede,am nevoie urgent,tot și dau 50 de puncte+coroană!!​​​

Answer 1

Explicație pas cu pas:

16.a)

$( - 2)^{6} = {2}^{6} > - {2}^{6}$

b)

${( - 3)}^{3} = - {3}^{3}$

c)

${( - 4)}^{0} = 1$

$- {4}^{0} = - 1$

$\implies {( - 4)}^{0} > - {4}^{0}$

d)

${( - {5}^{3} )}^{2} = {({5}^{3} )}^{2} = {5}^{6}$

$- {({5}^{3} )}^{2} = - {5}^{6}$

$\implies {( - {5}^{3} )}^{2} > \implies - {({5}^{3} )}^{2}$

e)

${( - {6}^{4} )}^{7} = - {6}^{28}$

$- {36}^{14} = - {({6}^{2} )}^{14} = - {6}^{28}$

$\implies {( - {6}^{4} )}^{7} = - {36}^{14}$

f)

${( - 8)}^{24} = {8}^{24}$

${( - 64)}^{12} = {( - {8}^{2} )}^{12} = {8}^{24}$

$\implies {( - 8)}^{24} = {( - 64)}^{12}$

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}

$S = ( - 4) + ( - 3) + ... + 0 + 1 + 2+ ... + 13 \\ = - (4 + 3 + 2 + 1) + 0 + 1 + 2 + ... + 13 \\ = \frac{13 \times 14}{2} - \frac{4 \times 5}{2} = \frac{182 - 20}{2} = \frac{162}{2} = 81$

b) |x| < 20, x ∈ Z => -20 < x < 20

=> x ∈ {-19, -18, ..., 18, 19}

$S = ( - 19) + ( - 18) + ... + ( - 1) + 0 + 1 + ... + 18 + 19 \\ = - (19 + 18 + ... + 2 + 1) + 0 + (1 + 2 + ... + 18 + 19) \\ = \frac{19 \times 20}{2} - \frac{19 \times 20}{2} = 0$

19.

- 8° - 3° = - 12°