The problem asks for an equivalent form of the expression:

$\left( \frac{3}{5} \right)^{-10}$

When dealing with negative exponents, the rule to remember is:

$a^{-n} = \frac{1}{a^n}$

Thus, the expression $\left( \frac{3}{5} \right)^{-10}$ becomes:

$\frac{1}{\left( \frac{3}{5} \right)^{10}}$

This can be rewritten as:

$\frac{1}{\left( \frac{3^{10}}{5^{10}} \right)} = \frac{5^{10}}{3^{10}}$

Now, let's look at the choices:

• $\left( \frac{5}{3} \right)^{10}$
• $- \frac{310}{5}$
• $\frac{5^{10}}{3^{10}}$
• $- \left( \frac{3}{5} \right)^{10}$

The correct equivalent form is: $\frac{5^{10}}{3^{10}}$.

Would you like a more detailed explanation of how this transformation works, or do you have any other questions?

Further Questions:

1. What is the result of $\left( \frac{2}{3} \right)^{-5}$?
2. How do we handle negative exponents when applied to variables in algebra?
3. Can you simplify the expression $\left( \frac{4}{7} \right)^{-3}$?
4. How would you express $\left( 2x \right)^{-4}$ in terms of positive exponents?
5. What is the general rule for dealing with negative exponents in rational expressions?

Tip: Remember that a negative exponent indicates the reciprocal of the base raised to the positive exponent.