The expression from the image you've uploaded appears to be the following:

$\left(\frac{3}{4}\right)^{-4} \cdot 0.09^{-0.5} - 7.5 \cdot 4^{\frac{5}{3}} \cdot (-2)^{-4}$

Let me break this down step-by-step and compute the value.

Terms in the expression:

1. $\left(\frac{3}{4}\right)^{-4}$
2. $0.09^{-0.5}$
3. $7.5 \cdot 4^{\frac{5}{3}}$
4. $(-2)^{-4}$

I'll solve each of these components and provide the final result. Let's start with the calculations.The result of the expression

$\left(\frac{3}{4}\right)^{-4} \cdot 0.09^{-0.5} - 7.5 \cdot 4^{\frac{5}{3}} \cdot (-2)^{-4}$

is approximately 5.81.

Would you like further explanation on any part of the solution?

Here are 5 related questions for further exploration:

1. How do fractional exponents affect numbers?
2. What is the significance of negative exponents in expressions?
3. Can you explain how to simplify powers of fractions like $\left(\frac{3}{4}\right)^{-4}$?
4. How do you calculate fractional powers like $4^{\frac{5}{3}}$?
5. Why does $(-2)^{-4}$ give a positive result?

Tip: When dealing with negative exponents, think of them as reciprocals. For example, $x^{-n} = \frac{1}{x^n}$.