https://file.aiquickdraw.com/mathbot/file/1725758651033u3jokg4y.jpg

I see that you've uploaded an image showing some math-related content. Let me examine the image and extract the relevant information.

I will take a moment to process it.The image you uploaded contains a question from a quiz review. From the visible content, it appears to be a section called "P.1 Quiz Review," with an exercise asking for simplification or computation of expressions involving exponents and/or other algebraic terms.

The current question visible is:

\[
\left( \dfrac{x^{3}}{x^{5}} \right)^{3}
\]

The answer box shows calculations like:

- The operation seems to involve simplifying the expression by applying exponent rules.

### Let's solve the expression step-by-step:

1. First, simplify the fraction \(\frac{x^3}{x^5}\). By the rule of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we have:
   \[
   \frac{x^3}{x^5} = x^{3-5} = x^{-2}
   \]

2. Next, raise this result to the power of 3:
   \[
   \left(x^{-2}\right)^3 = x^{-2 \times 3} = x^{-6}
   \]

Thus, the simplified expression is:

\[
x^{-6}
\]

This can also be written as \(\frac{1}{x^6}\), depending on how your instructor prefers answers to be formatted.

Would you like any further clarification or details?

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Here are five related questions that might help deepen your understanding:

1. How do you simplify expressions with exponents when the base is the same?
2. What are the rules for multiplying exponents when raising a power to another power?
3. How do negative exponents affect the expression? How can they be rewritten?
4. Can you apply the same exponent rules to fractions involving variables and numbers?
5. What happens when an exponent is zero? How do you simplify such expressions?

**Tip**: Always remember the key exponent rule \(\frac{a^m}{a^n} = a^{m-n}\) when dealing with division of powers with the same base!

Simplify the algebraic expression (x^3 / x^5)^3 using exponent rules. This problem focuses on dividing powers with the same base and raising powers to another power, suitable for students in Grades 8-10.

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