The expression in the image is:

$\left(\frac{x^{-3}}{y^3}\right)^{-7}$

To simplify this expression, let's follow the steps below:

1. Apply the Negative Exponent Rule: Recall that $a^{-n} = \frac{1}{a^n}$. This rule applies to both the fraction and the exponent:

   $\left(\frac{x^{-3}}{y^3}\right)^{-7} = \left(\frac{y^3}{x^{-3}}\right)^{7}$

2. Simplify the Fraction Inside the Parentheses: Since $x^{-3} = \frac{1}{x^3}$, the fraction becomes:

   $\frac{y^3}{\frac{1}{x^3}} = y^3 \cdot x^3 = x^3y^3$

3. Apply the Exponent to Each Term: Distribute the exponent of 7 to both $x^3$ and $y^3$:

   $\left(x^3y^3\right)^7 = (x^3)^7 \cdot (y^3)^7 = x^{21} \cdot y^{21}$

Thus, the simplified form of the expression is:

$x^{21}y^{21}$

Would you like any more details or have any questions?

Here are five related questions:

1. How would you simplify $\left(\frac{x^2}{y^{-5}}\right)^{-3}$?
2. What happens when you have a negative exponent outside the parentheses for a fraction?
3. How do you simplify expressions with multiple negative exponents?
4. What is the general rule for distributing exponents over products?
5. Can you simplify $\left(\frac{x^m}{y^n}\right)^{-k}$ for general $m$, $n$, and $k$?

Tip: Always remember to handle negative exponents carefully by applying the rule $a^{-n} = \frac{1}{a^n}$ before simplifying the expression further.