The number of digits in the decimal expansion of $16^{5} 5^{16}$ is

16

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17

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18

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19

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Solution

The correct option is C $18$
$16^{5} 5^{16}$
$= 2^{20} 5^{16}$
$= 10^{16} 2^{4}$
$= 16 \times 10^{16}$
$= 1.6 \times 10^{17}$
Number of digits in the integer $m \times 10^{n}$ , where $1 \leq m < 10$ , is $n + 1$ .

Hence number of digits = 18

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The number of digits in the decimal expansion of 165516 is

The correct option is C 18165516=220516=101624=16×1016=1.6×1017Number of digits in the integer m×10n, where 1≤m<10, is n+1.Hence number of digits = 18

The number of digits in the decimal expansion of $16^{5} 5^{16}$ is

The correct option is C $18$
$16^{5} 5^{16}$
$= 2^{20} 5^{16}$
$= 10^{16} 2^{4}$
$= 16 \times 10^{16}$
$= 1.6 \times 10^{17}$
Number of digits in the integer $m \times 10^{n}$ , where $1 \leq m < 10$ , is $n + 1$ .

Hence number of digits = 18