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 $18$
$16^{5} \times 5^{16} = 2^{20} \times 5^{16} = 2^{4} \times (2 \times 5)^{16} = 16 \times 10^{16} \Rightarrow 2 + 16 = 18 digits$

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The number of digits in the decimal expansion of 165516 is

The correct option is C 18 165×516=220×516=24×(2×5)16=16×1016⇒2+16=18 digits

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

The correct option is C $18$
$16^{5} \times 5^{16} = 2^{20} \times 5^{16} = 2^{4} \times (2 \times 5)^{16} = 16 \times 10^{16} \Rightarrow 2 + 16 = 18 digits$