Let's evaluate the expressions given in the image step by step.

Expression 1:

$\left( \frac{2}{3} \right)^{-0.75}$

To compute:

1. Calculate $\frac{2}{3}$ which is approximately 0.6667.
2. Raise $0.6667$ to the power of $-0.75$.

$\left( \frac{2}{3} \right)^{-0.75} = (0.6667)^{-0.75}$

Using a calculator: $(0.6667)^{-0.75} \approx 1.395.$

Expression 2:

$3.2^{1.5}$

To compute:

1. Calculate $3.2^{1.5}$ directly using a calculator.

Using a calculator: $3.2^{1.5} = 3.2^{\frac{3}{2}} = (3.2 \cdot \sqrt{3.2}) \approx 5.722.$

Final Results:

1. $\left( \frac{2}{3} \right)^{-0.75} \approx 1.395$
2. $3.2^{1.5} \approx 5.722$

Let me know if you need detailed steps or have any questions!

Here are 5 related questions for further learning:

1. What is the significance of negative exponents in expressions?
2. How is a fractional exponent like $1.5$ related to roots and powers?
3. Can you calculate $\left( \frac{3}{4} \right)^{-0.5}$?
4. How can we simplify $x^{-n}$ into fractions for easier computation?
5. How do scientific calculators handle fractional powers like $2^{2.3}$?

Tip: Remember that $a^{-n} = \frac{1}{a^n}$, which can help simplify calculations!