It looks like you're working with an expression involving exponents. Here's a breakdown of the expressions you're working with:

Part (a):

Simplify $\left(\frac{5}{7}\right)^{3}$

This expression involves raising a fraction to the power of 3. We apply the power to both the numerator and denominator:

$\left(\frac{5}{7}\right)^3 = \frac{5^3}{7^3} = \frac{125}{343}$

Part (b):

Simplify $\left(\frac{24}{7}\right)^{-3}$

A negative exponent indicates we take the reciprocal and then apply the positive exponent:

$\left(\frac{24}{7}\right)^{-3} = \frac{7^3}{24^3} = \frac{343}{13824}$

Part (c):

Simplify $\left(\frac{7}{5}\right)^{2}$

This is a simple power of a fraction:

$\left(\frac{7}{5}\right)^2 = \frac{7^2}{5^2} = \frac{49}{25}$

Part (d):

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

Here, raise the negative fraction to the power of 3:

$\left(\frac{-3}{2}\right)^3 = \frac{(-3)^3}{2^3} = \frac{-27}{8}$

Part (e):

Simplify $\left(\frac{32}{27}\right)^{2/3}$

This is a fractional exponent. First, take the cube root of 32 and 27, then square the result:

$\left(\frac{32}{27}\right)^{2/3} = \left(\frac{2^5}{3^3}\right)^{2/3} = \left(\frac{2}{3}\right)^2 = \frac{4}{9}$

These are the simplified results for the expressions.

Would you like further explanation or clarification on any of these steps? Here are some related questions:

1. What is the rule for simplifying expressions with negative exponents?
2. How can you handle fractional exponents more effectively?
3. How do you simplify powers of negative numbers in fractions?
4. What is the general approach to simplifying powers of fractions?
5. Can you apply the same method to simplify roots in similar expressions?

Tip: When simplifying expressions with negative exponents, remember that the negative sign in the exponent means you need to flip the base (take the reciprocal) and then apply the positive exponent.