Question

comparați numerele . 2 la puterea 72 si 4 la puterea 37 10 la puterea 100 si 100 la putere 10 9 la puterea 30 si 27 la puterea 10 32 la puterea 20 si 16 25 ,9 la puterea 40 si 81 20 , 3 la puterea 45 si 2 30​

Answer 1

Răspuns:

${4}^{37} = ( {2}^{2} )^{37} = {2}^{74} = > {2}^{72} < {4}^{37}$

${100}^{10} = ( {10}^{2} )^{10} = {10}^{20} = > {10}^{100} > {100}^{10}$

${9}^{30} = ( {3}^{2} )^{30} = {3}^{60}$

${27}^{10} = ( {3}^{3} )^{10} = {3}^{30} = > {9}^{30} > {27}^{10}$

${32}^{20} = ( {2}^{5} )^{20} = {2}^{100}$

${16}^{25} = ( {2}^{4} )^{25} = {2}^{100} = > {32}^{20} = {16}^{25}$

${9}^{40} = ( {3}^{2} )^{40} = {3}^{80}$

Mai departe nu mai înțeleg care sunt bazele și care sunt exponenții...

Answer 2

Răspuns:

$\bf {4}^{37} = \big( {2}^{2} \big)^{37} = {2}^{74} \Rightarrow \blue{\underline{~{2}^{72}~< ~{4}^{37}}}$

                                             

$\bf {100}^{10} = \big( {10}^{2} \big)^{10} = {10}^{20} \Rightarrow\green{\underline{~{10}^{100} ~>~ {100}^{10}}}$

                                             

$\bf {9}^{30} = \big( {3}^{2} \big)^{30} = {3}^{60}$

$\bf {27}^{10} = \big( {3}^{3} \big)^{10} = {3}^{30} \Rightarrow\purple{\underline{~{9}^{30} ~> ~{27}^{10}}}$

                                             

$\bf {32}^{20} = \big( {2}^{5} \big)^{20} = {2}^{100}$

$\bf {16}^{25} = \big( {2}^{4} \big)^{25} = {2}^{100} \Rightarrow\pink{\underline{~{32}^{20} = {16}^{25}}}$

                                             

$\bf {9}^{40} = \big( {3}^{2} \big)^{40} = {3}^{80}$

$\bf {81}^{20} = \big( {3}^{4} \big)^{20} = {3}^{80} \Rightarrow\red{\underline{~{9}^{40} ={81}^{20}}}$