Two And Two Makes What?

Algebra Level 1

Which of these numbers is the largest?

$\Large {\begin{aligned} A &= &2^{222} \\ B &= &2^{22^2} \\ C &= &2^{2^{22}} \end{aligned} }$

A

B

C

4 solutions

Chew-Seong Cheong
Sep 3, 2016

$A = 2^{222}$ , $B = 2^{22^2} = 2^{484}$ , $C = 2^{2^{22}} > 2^{2^9} = 2^{512}$ $\implies A<B<\boxed{C}$ .

Sabhrant Sachan
Sep 3, 2016

$\text{Since } 222<22^2<2^{22} \\ \implies 2^{222} <2^{22^{2}} < 2^{2^{22}}$

Mohammad Khaza
Jul 2, 2017

A=2^222

B=2^22^2=2^484

C=2^2^22=2^512

so,C>B>A

Akash Mishra
Sep 6, 2016

Use the indices rule to solve it