Question

3. Comparând numerele a=(-3)5²:3 şi b=272: (-8): (22)5 obţinem:
a)-a b) azb
c) -a>b
d) -a>-b

Answer 1

Răspuns:

- a > - b

Explicație pas cu pas:

$a = {( - 3)}^{ {5}^{2} } : 3 = {( - 3)}^{25} : 3 = - {3}^{25} : 3 = - {3}^{24} = - {3}^{2 \cdot 12} = - {( {3}^{2} )}^{12} = \bf - {9}^{12}$

$b = {2}^{ {7}^{2} } : ( - 8) : {( {2}^{2} )}^{5} = {2}^{49} : ( - {2}^{3} ) : {2}^{10} = - {2}^{46} : {2}^{10} = - {2}^{36} = - {2}^{3 \cdot 12} = - {( {2}^{3} )}^{12} = \bf - {8}^{12}$

$- {9}^{12} < - {8}^{12} \implies a < b \iff \bf - a > - b$