Question

The largest number among the following is

• A. $3^{2^{2^{2^2}}}$
• B. ${\left\{{\left(3^2\right)}^2\right\}}^2$
• C. $3^2\times 3^2\times 3^2$
• D. $3222$

Answer 1

The correct option is A $3^{2^{2^{2^2}}}$

$1)3^{2^{2^{2^2}}}=3^{2^{2^4}}=3^{16}$

$2){\left\{{\left(3^2\right)}^2\right\}}^2=3^8=6561$

$3)3^2\times 3^2\times 3^2=3^{2+2+2}=3^6=729$

$\therefore 3^{2^{2^{2^2}}}>{\left\{{\left(3^2\right)}^2\right\}}^2>3222>3^2\times 3^2\times 3^2$

The largest number among the above is $3^{2^{2^{2^2}}}$.