[tex]\bf 5^{22} = \big(5^{2}\big)^{11} = 25^{11}[/tex]
[tex]\bf 2^{55} = \big(2^{5}\big)^{11} = 32^{11}[/tex]
[tex]\bf 25^{11}~<32^{11}\implies \blue{\underline{5^{22}~<~2^{22}}}[/tex]
[tex]\bf 5^{33} = \big(5^{3}\big)^{11} = 125^{11}[/tex]
[tex]\bf 3^{55} = \big(3^{5}\big)^{11} = 243^{11}[/tex]
[tex]\bf 125^{11}~<~243^{11}\implies \pink{\underline{5^{33}~<~3^{55}}}[/tex]
[tex]\bf 4^{39} = \big(4^{3}\big)^{13} = 64^{13}[/tex]
[tex]\bf 5^{26} = \big(5^{2}\big)^{13} = 25^{13}[/tex]
[tex]\bf 64^{13}~>~25^{13}\implies \green{\underline{4^{39}~>~5^{26}}}[/tex]
[tex]\bf 4^{22} = \big(2^{2}\big)^{11} = 4^{11}[/tex]
[tex]\bf 2^{44} = \big(2^{4}\big)^{11} = 16^{11}[/tex]
[tex]\bf 4^{11}~<~16^{11}\implies \green{\underline{4^{11}~<~2^{44}}}[/tex]
[tex]\bf 2^{44} = \big(2^{4}\big)^{11} = 16^{11}[/tex]
[tex]\bf 5^{33} = \big(5^{3}\big)^{11} = 125^{11}[/tex]
[tex]\bf 16^{11}~<~125^{11}\implies \red{\underline{2^{44}~<~5^{33}}}[/tex]
[tex]\bf 2^{45} = \big(2^{3}\big)^{15} = 8^{15}[/tex]
[tex]\bf 3^{30} = \big(3^{2}\big)^{15} = 9^{15}[/tex]
[tex]\bf 8^{15}~<~9^{15}\implies \purple{\underline{2^{45}~<~3^{30}}}[/tex]
[tex]==pav38==[/tex]
