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Question

The largest number among the following is


A
32222
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B
{(32)2}2
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C
32×32×32
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D
3222
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Solution

The correct option is A $$\displaystyle 3^{2^{2^{2^2}}}$$
$$1) 3^{2^{2^{2^{2}}}}=3^{2^{2^{4}}}=3^{16}$$

$$ 2) \left \{ \left ( 3^{2} \right )^{2} \right \}^{2}=3^{8}=6561$$
$$ 3) 3^{2}\times 3^{2}\times 3^{2}=3^{2+2+2}=3^{6}=729$$
$$ \therefore 3^{2^{2^{2^{2}}}}>\left \{ \left ( 3^{2} \right )^{2} \right \}^{2}>3222>3^{2}\times 3^{2}\times 3^{2}$$

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

Mathematics

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