The value of the given expression:

$81^{3/4} + \frac{1}{\sqrt{4^{-1}}} + 64^{1/3} - \frac{3}{27^{-1/3}} - \frac{2}{16^{3/4}}$

is approximately $23.75$. However, since this value does not match any of the options provided, it seems there may be a discrepancy in the options or a miscalculation in the provided question.

Would you like to explore any part of the calculation in more detail?

Here are 5 related questions that could further your understanding:

1. How do we simplify fractional exponents in different bases?
2. What is the general formula for converting between roots and fractional exponents?
3. How can we simplify complex terms involving both square roots and cube roots?
4. How does changing the sign of the exponent (positive vs negative) affect the value of the term?
5. What are common pitfalls when simplifying large fractional exponent expressions?

Tip: When working with roots and exponents, remember that $a^{m/n} = \sqrt[n]{a^m}$. This can help in converting and simplifying complex terms.