Question

pliz cele 2 exerciti incercuite

Answer 1

Explicație pas cu pas:

8.a)

$(2 \cdot {2}^{1} \cdot {2}^{2} \cdot ... \cdot {2}^{50}) : {( {2}^{17} )}^{75} = {2}^{1 + 2 + ... + 50} : {2}^{17 \cdot 75} = {2}^{ \frac{50 \cdot 51}{2} } : {2}^{1275} = {2}^{1275} : {2}^{1275} = \bf 1$

b)

$( {9}^{2} \cdot {9}^{4} \cdot {9}^{6} \cdot ... \cdot {9}^{80}) : ( {3}^{1} \cdot {3}^{2} \cdot {3}^{3} \cdot ... \cdot {3}^{50}) = {9}^{2 + 4 + 6 + ... + 80} : {3}^{1 + 2 + 3 + ... + 50} = {( {3}^{2} )}^{2 \cdot (1 + 2 + 3 + ... + 40)} : {3}^{ \frac{50 \cdot 51}{2} } = {3}^{2 \cdot 2 \cdot \frac{40 \cdot 41}{2} } : {3}^{1275} = {3}^{3280} : {3}^{1275} = {3}^{3280 - 1275} = \bf {3}^{2005}$

c)

$( {5}^{1} \cdot {5}^{3} \cdot {5}^{5} \cdot ... \cdot {5}^{99}) : ( {5}^{5} \cdot {5}^{10} \cdot {5}^{15} \cdot ... \cdot {5}^{150}) = {5}^{1 + 3 + 5 + ... + 99} : {5}^{5 + 10 + 15 + ... + 150} = {5}^{ {50}^{2} } : {5}^{5 \cdot (1 + 2 + 3 + ... + 30)} = {5}^{2500} : {5}^{5 \cdot \frac{30 \cdot 31}{2} } = {5}^{2500} : {5}^{2325} = {5}^{2500 - 2325} = \bf {5}^{175}$