Let's go through each of the problems in the image and solve them one by one:

1. $\left(\frac{3}{5}\right)^3$ $= \frac{3^3}{5^3} = \frac{27}{125}$

2. $(-7)^4$ $= 7^4 = 2401$

3. $-5^4$ $= -(5^4) = -625$

4. $\frac{9}{4} \times \left(\frac{2}{3}\right)^2$ $= \frac{9}{4} \times \frac{4}{9} = 1$

5. $\left(\frac{-2}{5}\right)^2 \times \left(\frac{-5}{2}\right)^3 \times \left(\frac{1}{5}\right)^0$

   = \frac{4 \times (-125)}{25 \times 8} = \frac{-500}{200} = -\frac{5}{2}$$

6. $\left(\frac{1}{5}\right)^2 \times \left(\frac{-2}{1}\right)^3$ $= \frac{1}{25} \times (-8) = \frac{-8}{25}$

7. $2^{7/9} \div \left(1 \frac{2}{3}\right)^2$ First, convert $1 \frac{2}{3}$ to an improper fraction: $1 \frac{2}{3} = \frac{5}{3}$ $2^{7/9} \div \left(\frac{5}{3}\right)^2 = 2^{7/9} \div \frac{25}{9} = 2^{7/9} \times \frac{9}{25}$

8. $(-2)^4 + (-3)^3$ $= 16 + (-27) = -11$

9. $(-1)^{50} + (-1)^{99}$ $= 1 + (-1) = 0$

10. $2^3 + 2^2$ $= 8 + 4 = 12$

11. $(0.3)^2 \times 3^{-2}$ $= 0.09 \times \frac{1}{9} = \frac{0.09}{9} = 0.01$

These are the simplified forms of the expressions.

Let me know if you'd like further details or clarification on any of the steps!

Here are some related questions:

1. What is the rule for multiplying or dividing powers with the same base?
2. How do negative exponents work?
3. How do you simplify expressions with fractional exponents?
4. What are the properties of exponents for different bases?
5. Can you solve similar problems involving large exponents?

Tip: When simplifying expressions with exponents, always look for opportunities to apply exponent rules, like the power of a power or the product of powers rules!