To simplify the expression \( \left(\frac{27^3}{9^5}\right) \), let's break it down:

1. First, express 27 and 9 as powers of 3:
   \[
   27 = 3^3 \quad \text{and} \quad 9 = 3^2
   \]

2. Now substitute these into the expression:
   \[
   \left(\frac{27^3}{9^5}\right) = \frac{(3^3)^3}{(3^2)^5}
   \]

3. Simplify the powers:
   \[
   \frac{(3^9)}{(3^{10})} = 3^{9-10} = 3^{-1}
   \]

4. Finally, simplify \( 3^{-1} \):
   \[
   3^{-1} = \frac{1}{3}
   \]

Thus, the simplified form of the expression is \( \frac{1}{3} \).

Do you want more details or have any questions?

Here are some related questions:
1. How do you simplify expressions with powers and roots?
2. What are the rules for multiplying and dividing powers?
3. How do you convert negative exponents into fractions?
4. What happens when you raise a power to another power?
5. How do you deal with complex expressions involving multiple bases?

**Tip:** When working with powers, always try to express all numbers with the same base to make simplification easier!

Learn how to simplify the expression (27^3 / 9^5) step-by-step with detailed explanations. This problem involves exponentiation and fractional exponents. Suitable for students in Grades 9-12.

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