The product of divisors of 512 is

The product of divisors of 512 is

A
$2^{45}$
B
$2^{54}$
C
$2^{100}$
D
$2^{2^{100}}$

Solution:

$512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$512 = 2^{9}$

Number of divisors $d (512) = 9 + 1 = 10$

Product of divisors $N = N^{\frac{1}{2} d (N)}$

Product of divisors of $512 = 512^{\frac{1}{2} \times 10}$

$= 512^{5}$

$= {(2^{9})}^{5}$

$= 2^{45}$

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