Question

in the expansion 16^5×5^16 find the number of digits

Answer 1

we can rewrite this as

$=( 16^{5} )( 5^{16} )$

$=( 2^{20} )( 5^{16} )$

$=( 2^{4} )( 2^{16}* 5^{16} )$

$=( 16 )( (2*5)^{16} )$

$= 16*10^{16}$

Number of digits in 16x10^1 are 3 .
The number of digits in 16x10^2) are 4 .
The number of digits in 16x10^3) are 5.
Therefore, the number of digits of 16x10^16will be 18

Answer 2

Hey mate......✌

Here's ur ans. ⬇

↪
$16 {}^{5} \times 5 {}^{16}$

$(2 {}^{4} ) {}^{5} \times 5 {}^{16}$

$2 {}^{20} \times 5 {}^{16}$

$2 {}^{4} \times {2}^{16} \times 5 {}^{16}$

${2}^{4} \times ( {2}^{16} \times {5}^{16} )$

$2 {}^{4} \times (2 \times 5) {}^{16}$


$16 \times {10}^{16}$

Hence, total no. of digits = 18

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.✌Hope it helps