Question

Ordonaţi crescător numerele: 333 (3³)³, 33³, 333.​

Answer 1

1.(3³)³ 2.3³^³ 3.33³ 4. 3³³

Answer 2

Explicație pas cu pas:

${3}^{ {3}^{3} } = {3}^{27}$

${( {3}^{3} )}^{3} = {3}^{9}$

${3}^{9} = {( {3}^{3})}^{3} = {27}^{3} \\ {3}^{12} = {( {3}^{4})}^{3} = {81}^{3} \\ {27}^{3} < {33}^{3} < {81}^{3}$

$\implies {3}^{9} < {33}^{3} < {3}^{12}$

atunci:

${3}^{9} < {33}^{3} < {3}^{27} < {3}^{33}$

rezultă că:

$\bf {( {3}^{3} )}^{3} < {33}^{3} < {3}^{ {3}^{3} } < {3}^{33}$