The expression given is:

$\left(\frac{5^2}{3^3}\right)^3$

To simplify this:

1. Start by simplifying the inner part: $5^2 = 25 \quad \text{and} \quad 3^3 = 27$ So the fraction becomes: $\frac{25}{27}$

2. Raise this fraction to the power of 3: $\left(\frac{25}{27}\right)^3 = \frac{25^3}{27^3}$

3. Calculate $25^3$ and $27^3$:

   • $25^3 = 25 \times 25 \times 25 = 15625$
   • $27^3 = 27 \times 27 \times 27 = 19683$

Thus, the simplified numerical expression is:

$\frac{15625}{19683}$

Let me know if you'd like further explanations or if you have more questions!

Here are five related questions to explore:

1. How do you simplify expressions with exponents in the numerator and denominator?
2. What are the properties of exponents used in similar problems?
3. How do you evaluate higher powers like $25^3$ or $27^3$ efficiently?
4. Can you represent $\frac{15625}{19683}$ in decimal form for comparison?
5. How would this process change if the base numbers (5 and 3) were replaced with variables?

Tip: When simplifying exponentiation, always resolve the inner terms before applying the outer exponent to avoid unnecessary complexity.