2019 2019 Exponents

Algebra Level 2

Which is bigger

A = 201 9 ( 201 9 2019 ) or B = ( 201 9 2019 ) 2019 ? \large A=2019^{\left(2019^{2019}\right)} \quad \text{or} \quad B=\left({2019^{2019}}\right)^{2019}?

B > A B > A A > B A > B A = B A = B

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2 solutions

B = ( 201 9 2019 ) 2019 = 201 9 2019 2019 B=({2019^{2019}})^{2019}=2019^{2019 \cdot 2019}

201 9 2019 > 2019 2019 2019^{2019} > 2019 \cdot 2019 .

So A > B \boxed{A>B} .

Chew-Seong Cheong
Dec 28, 2018

B = ( 201 9 2019 ) 2019 = 201 9 201 9 2 < 201 9 201 9 2019 A > B B = \left(2019^{2019}\right)^{2019} = 2019^{2019^2} < 2019^{2019^{2019}} \implies \boxed {A>B}

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