Question

URGENT PENTRU MÂINE!!​

Answer 1

Explicație pas cu pas:

a)

$a = {2}^{36} = {2}^{3 \cdot 12} = {({2}^{3} )}^{12} = {8}^{12}$

$b = {3}^{24} = {3}^{2 \cdot 12} = {({3}^{2} )}^{12} = {9}^{12}$

${8}^{12} < {9}^{12} \implies a < b$

b)

$a = {3}^{30} = {3}^{3 \cdot 10} = {({3}^{3} )}^{10} = {27}^{10}$

$b = {5}^{20} = {5}^{2 \cdot 10} = {({5}^{2} )}^{10} = {25}^{10}$

${27}^{10} > {25}^{10} \implies a > b$

c)

$a = {11}^{50} = {11}^{2 \cdot 25} = {({11}^{2} )}^{25} = {121}^{25}$

$b = {5}^{75} = {5}^{3 \cdot 25} = {({5}^{3} )}^{25} = {125}^{25}$

${121}^{25} < {125}^{25} \implies a < b$

d)

$a = {3}^{33} = {3}^{3 \cdot 11} = {({3}^{3} )}^{11} = {27}^{11}$

$b = {2}^{55} = {2}^{5 \cdot 11} = {({2}^{5} )}^{11} = {32}^{11}$

${27}^{11} < {32}^{11} \implies a < b$