MATL, 35 bytes

'nTIFBCAAAAA@A@A@A@@A'tfYqwIEW-^X$p

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Explanation

This uses the prime factorization of the number:

\$ 808017424794512875886459904961710757005754368000000000 \\ = 2^{46} · 3^{20} · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71. \$

'nTIFBCAAAAA@A@A@A@@A' % Push this string
t                      % Duplicate
f                      % Indices of all nonzero chars: gives [1 2 3 ... 19 20]
Yq                     % n-th prime, element-wise: gives [2 3 5 ... 67 71]
w                      % Swap
IEW                    % Push 3, multiply by 2, exponential with base 2: gives 64
-                      % Subtract, element-wise: subtracts 64 from the code point
                       % of each character of the string. Gives [46 20 9 ... 0 1]
^                      % Element-wise power. Gives [2^46 3^20 5^9 ... 1 71]
X$                     % Convert to symbolic (to achieve arbitrary precision)
p                      % Product. Implicit display 

MATL, 35 bytes

'nTIFBCAAAAA@A@A@A@@A'tfYqwIEW-^X$p

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Explanation

This uses the prime factorization of the number:

\$ 808017424794512875886459904961710757005754368000000000 \\ = 2^{46} · 3^{20} · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71. \$

'nTIFBCAAAAA@A@A@A@@A' % Push this string
t                      % Duplicate
f                      % Indices of nonzero chars: gives [1 2 3 ... 19 20]
Yq                     % n-th prime, element-wise: gives [2 3 5 ... 67 71]
w                      % Swap
IEW                    % Push 3, multiply by 2, exponential with base 2: gives 64
-                      % Subtract, element-wise: subtracts 64 from the code point
                       % of each character of the string. Gives [46 20 9 ... 0 1]
^                      % Element-wise power. Gives [2^46 3^20 5^9 ... 1 71]
X$                     % Convert to symbolic (to achieve arbitrary precision)
p                      % Product. Implicit display 

MATL, 35 bytes

'nTIFBCAAAAA@A@A@A@@A'tfYqwIEW-^X$p

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Explanation

This uses the fact that

\$2^{46} · 3^{20} · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 \\= 808017424794512875886459904961710757005754368000000000. \$

'nTIFBCAAAAA@A@A@A@@A' % Push this string
t                      % Duplicate
f                      % Indices of all nonzero chars: gives [1 2 3 ... 20]
Yq                     % n-th prime, element-wise: gives [2 3 5 ... 71]
w                      % Swap
IEW                    % Push 3, multiply by 2, exponential with base 2: gives 64
-                      % Subtract, element-wise: subtracts 64 from the code point
                       % of each character of the string. Gives [46 20 9 ... 1]
^                      % Element-wise power. Gives [2^46 3^20 5^9 ... 71]
X$                     % Convert to symbolic (to achieve arbitrary precision)
p                      % Product. Implicit display 

MATL, 35 bytes

'nTIFBCAAAAA@A@A@A@@A'tfYqwIEW-^X$p

Try it online!

Explanation

This uses the prime factorization of the number:

\$ 808017424794512875886459904961710757005754368000000000 \\ = 2^{46} · 3^{20} · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71. \$

'nTIFBCAAAAA@A@A@A@@A' % Push this string
t                      % Duplicate
f                      % Indices of all nonzero chars: gives [1 2 3 ... 19 20]
Yq                     % n-th prime, element-wise: gives [2 3 5 ... 67 71]
w                      % Swap
IEW                    % Push 3, multiply by 2, exponential with base 2: gives 64
-                      % Subtract, element-wise: subtracts 64 from the code point
                       % of each character of the string. Gives [46 20 9 ... 0 1]
^                      % Element-wise power. Gives [2^46 3^20 5^9 ... 1 71]
X$                     % Convert to symbolic (to achieve arbitrary precision)
p                      % Product. Implicit display 

MATL, 35 bytes

'nTIFBCAAAAA@A@A@A@@A'tfYqwIEW-^X$p

Try it online!

MATL, 35 bytes

'nTIFBCAAAAA@A@A@A@@A'tfYqwIEW-^X$p

Try it online!

Explanation

This uses the fact that

\$2^{46} · 3^{20} · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 \\= 808017424794512875886459904961710757005754368000000000. \$

'nTIFBCAAAAA@A@A@A@@A' % Push this string
t                      % Duplicate
f                      % Indices of all nonzero chars: gives [1 2 3 ... 20]
Yq                     % n-th prime, element-wise: gives [2 3 5 ... 71]
w                      % Swap
IEW                    % Push 3, multiply by 2, exponential with base 2: gives 64
-                      % Subtract, element-wise: subtracts 64 from the code point
                       % of each character of the string. Gives [46 20 9 ... 1]
^                      % Element-wise power. Gives [2^46 3^20 5^9 ... 71]
X$                     % Convert to symbolic (to achieve arbitrary precision)
p                      % Product. Implicit display