https://file.aiquickdraw.com/mathbot/file/1725418644955c65pp0wy.jpg

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?

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**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.

Simplify the expression: (x/y^2)^5 * (x^2y^3/z^2)^3

Learn how to simplify exponential expressions like (x/y^2)^5 * (x^2y^3/z^2)^3 with a detailed step-by-step approach. This example covers key algebraic concepts, including laws of exponents and multiplication of powers. Suitable for students in Grades 9-11.

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