The expression in the image can be interpreted and simplified as follows:

$\left(\frac{x}{y^2}\right)^5 \times \left(\frac{x^2y^3}{z^2}\right)^3$

Step 1: Apply the power to each term inside the parentheses.

1. For the first term $\left(\frac{x}{y^2}\right)^5$: $\frac{x^5}{y^{10}}$

2. For the second term $\left(\frac{x^2y^3}{z^2}\right)^3$: $\frac{(x^2)^3(y^3)^3}{(z^2)^3} = \frac{x^6 y^9}{z^6}$

Step 2: Multiply the simplified terms together.

$\frac{x^5}{y^{10}} \times \frac{x^6 y^9}{z^6}$

Multiply the numerators together and the denominators together:

$\frac{x^{5+6} y^9}{y^{10} z^6} = \frac{x^{11} y^9}{y^{10} z^6}$

Step 3: Simplify the expression by canceling common terms.

The $y$ terms in the numerator and denominator can be simplified:

$\frac{x^{11}}{y^{10-9} z^6} = \frac{x^{11}}{y z^6}$

Final Simplified Expression:

$\frac{x^{11}}{yz^6}$

Would you like any additional details or have any questions?

Here are 5 related questions:

1. How would the expression change if one of the exponents were negative?
2. Can you simplify an expression like $\left(\frac{a^3}{b^2}\right)^4 \times \left(\frac{b^5}{a^2}\right)^2$?
3. What happens if you have a variable in the denominator raised to a negative power?
4. How would you approach an expression with fractional exponents?
5. Can you explain how to apply the power rule to a product inside a fraction?

Tip: When simplifying expressions involving exponents, always apply the power to both the numerator and denominator, and then combine like terms carefully.