Identify the greater number, wherever possible, in the following?
$100^{2}$ or $2^{100}$ .

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Solution

Given $100^{2} o r 2^{100}$
$\Rightarrow 100^{2} = 100 \times 100 = 10, 000$
$\Rightarrow 2^{100} = 2 h u n d r e d t i m e s$
$\Rightarrow 2^{100} = 2^{80 + 10 + 10} = 2^{80} \times 2^{10} \times 2^{10}$
$\Rightarrow 2^{100} = k \times 1024 \times 1024$ where $k = 2^{80}$
$\Rightarrow 2^{100} = k \times 1024 \times 1024 > 10, 000$
Therefore $2^{100}$ is greater than $100^{2}$

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