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The expression to simplify is:

\[
\left( 3x^{-6}y^5 \right)^3
\]

We will simplify it step by step:

### Step 1: Apply the power of 3 to each term inside the parentheses.
For any expression \((a^m)^n\), the rule is that you multiply the exponents: \(a^{m \cdot n}\).

\[
\left( 3x^{-6}y^5 \right)^3 = 3^3 \cdot x^{-6 \cdot 3} \cdot y^{5 \cdot 3}
\]

### Step 2: Simplify each term.
\[
3^3 = 27
\]
\[
x^{-6 \cdot 3} = x^{-18}
\]
\[
y^{5 \cdot 3} = y^{15}
\]

### Step 3: Write the result.
The simplified expression is:

\[
27x^{-18}y^{15}
\]

Since the instruction asks for positive exponents, we'll write the final result with \(x^{-18}\) in the denominator:

\[
\frac{27y^{15}}{x^{18}}
\]

Thus, the final simplified expression is:

\[
\frac{27y^{15}}{x^{18}}
\]

Let me know if you would like further details or have any questions!

### Related Questions:
1. How do you simplify an expression with negative exponents?
2. What is the rule for raising a product to a power?
3. Can you explain the rule for multiplying exponents more generally?
4. How does the power of a product differ from the power of a quotient?
5. What happens when you raise a fraction to a negative exponent?

### Tip:
Always remember that a negative exponent means the reciprocal of the base raised to the corresponding positive exponent.

(3x^{-6}y^5)^3. Simplify the expression and write your answer using only positive exponents.

Learn how to simplify the expression (3x^{-6}y^5)^3 by applying exponentiation rules and expressing the final answer with only positive exponents. This problem covers key algebra concepts and is ideal for students in Grades 8-10.

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