64^-5÷6+(0.125) ^-1÷3-32*2^-4*16^-1^1÷2+(3^0) ^4*4

Let's break down the expression step by step:

1. \(64^{-5}\)
This is equal to \(1/64^5\), which is equal to \(1/(64*64*64*64*64)\), or \(1/1073741824\).

2. \(0.125^{-1}\)
This is equal to \(1/0.125\), which is equal to 8.

3. \(32*2^{-4}\)
This is equal to \(32*(1/2^4)\), which simplifies to \(32*(1/16)\), which is equal to 2.

4. \(16^{-1}\)
This is equal to \(1/16\), which is equal to 0.0625.

5. \(3^0\)
Any number raised to the power of 0 is equal to 1.

Now let's substitute these values back into the original expression:

\(1/1073741824 \div 6 + 8 \div 3 - 2 * 0.0625 * 1/2 + 1^4 * 4\)

Now we simplify further:

\(1/1073741824 \div 6 + 8/3 - 2 * 0.0625 * 1/2 + 1 * 4\)

\(1/1073741824 \div 6 + 8/3 - 2 * 0.0625 * 1/2 + 4\)

\(1/1073741824 \div 6 + 8/3 - 2 * 0.03125 + 4\)

\(1/1073741824 \div 6 + 8/3 - 0.0625 + 4\)

\(1/6442446944 + 2.66666666667 - 0.0625 + 4\)

Now, let's add up these values:

\(0.0000000001557 + 2.66666666667 - 0.0625 + 4\)

\(2.60416666633\)

Therefore, the final result of the expression is approximately 2.60416666633.