https://file.aiquickdraw.com/mathbot/file/1726402250938ckuorpoh.jpg

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, \(x^{-n} = \frac{1}{x^n}\).

Simplify the mathematical expression from the image: (3/4)^(-4) * 0.09^(-0.5) - 7.5 * 4^(5/3) * (-2)^(-4)

Learn how to simplify a complex expression involving fractional and negative exponents: (3/4)^(-4) * 0.09^(-0.5) - 7.5 * 4^(5/3) * (-2)^(-4). Explore key mathematical concepts such as exponents, laws of exponents, and properties of fractional powers.

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