Răspuns:
[tex] {4}^{37} = ( {2}^{2} )^{37} = {2}^{74} = > {2}^{72} < {4}^{37} [/tex]
[tex] {100}^{10} = ( {10}^{2} )^{10} = {10}^{20} = > {10}^{100} > {100}^{10} [/tex]
[tex] {9}^{30} = ( {3}^{2} )^{30} = {3}^{60} [/tex]
[tex] {27}^{10} = ( {3}^{3} )^{10} = {3}^{30} = > {9}^{30} > {27}^{10} [/tex]
[tex] {32}^{20} = ( {2}^{5} )^{20} = {2}^{100} [/tex]
[tex] {16}^{25} = ( {2}^{4} )^{25} = {2}^{100} = > {32}^{20} = {16}^{25} [/tex]
[tex] {9}^{40} = ( {3}^{2} )^{40} = {3}^{80} [/tex]
Mai departe nu mai înțeleg care sunt bazele și care sunt exponenții...
Răspuns:
[tex]\bf {4}^{37} = \big( {2}^{2} \big)^{37} = {2}^{74} \Rightarrow \blue{\underline{~{2}^{72}~< ~{4}^{37}}}[/tex]
[tex]\bf {100}^{10} = \big( {10}^{2} \big)^{10} = {10}^{20} \Rightarrow\green{\underline{~{10}^{100} ~>~ {100}^{10}}}[/tex]
[tex]\bf {9}^{30} = \big( {3}^{2} \big)^{30} = {3}^{60}[/tex]
[tex]\bf {27}^{10} = \big( {3}^{3} \big)^{10} = {3}^{30} \Rightarrow\purple{\underline{~{9}^{30} ~> ~{27}^{10}}}[/tex]
[tex]\bf {32}^{20} = \big( {2}^{5} \big)^{20} = {2}^{100}[/tex]
[tex]\bf {16}^{25} = \big( {2}^{4} \big)^{25} = {2}^{100} \Rightarrow\pink{\underline{~{32}^{20} = {16}^{25}}}[/tex]
[tex]\bf {9}^{40} = \big( {3}^{2} \big)^{40} = {3}^{80}[/tex]
[tex]\bf {81}^{20} = \big( {3}^{4} \big)^{20} = {3}^{80} \Rightarrow\red{\underline{~{9}^{40} ={81}^{20}}}[/tex]
