a) 3⁴⁰ = ( 3² )²⁰ = 9²⁰; 4⁴⁰ = ( 4² )²⁰ = 16²⁰; 7²⁰
16²⁰ > 9²⁰ > 7²⁰ ==> 4⁴⁰ > 3⁴⁰ > 7²⁰
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b)
5²² = ( 5² )¹¹ = 25¹¹
2⁵⁵ = ( 2⁵ )¹¹ = 32¹¹
3³³ = ( 3³ )¹¹ = 27¹¹
32¹¹ > 27¹¹ > 25¹¹ ==> 2⁵⁵ > 3³³ > 5²²
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c)
71³¹ ; 4⁹³ = ( 4³)³¹ = 64³¹; 7⁶² = ( 7² )³¹ = 49³¹
==> 71³¹ > 64³¹ > 49³¹ ==> 71³¹ > 4⁹³ > 7⁶²
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d) 20⁴⁰ = ( 20⁴ )¹⁰ = 160000¹⁰
40²⁰ = ( 40² ) ¹⁰ = 1600¹⁰
30³⁰ = (30³ )¹⁰ = 27000¹⁰
==>160000¹⁰ > 27000¹⁰ > 1600¹⁰
==> 20⁴⁰ > 30³⁰ > 40²⁰
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e) 3⁴⁰⁴ = ( 3⁴ )¹⁰¹ = 81¹⁰¹
2⁷⁰⁷ = ( 2⁷ )¹⁰¹ = 128¹⁰¹
5³⁰³ = ( 5³ )¹⁰¹ = 125¹⁰¹
==> 128¹⁰¹ > 125¹⁰¹ > 81¹⁰¹ ==> 2⁷⁰⁷ > 5³⁰³ > 3⁴⁰⁴
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f)
6⁵; 216³ = ( 6³ )³ = 6⁹; 36⁷ = ( 6² )⁷ = 6¹⁴
==> 6¹⁴ > 6⁹ > 6⁵ ==> 36⁷ > 216³ > 6⁵