Let's solve the expression \(\frac{27^3}{9^5}\).

1. First, we can express 27 and 9 in terms of powers of 3:
   \[
   27 = 3^3 \quad \text{and} \quad 9 = 3^2
   \]
   So, the expression becomes:
   \[
   \frac{(3^3)^3}{(3^2)^5}
   \]

2. Simplify the exponents:
   \[
   \frac{3^{3 \times 3}}{3^{2 \times 5}} = \frac{3^9}{3^{10}}
   \]

3. Apply the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\):
   \[
   3^{9-10} = 3^{-1}
   \]

4. Simplify further:
   \[
   3^{-1} = \frac{1}{3}
   \]

So, the final answer is \(\frac{1}{3}\).

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:
1. What is the result of \(\frac{81^2}{27^3}\)?
2. How do you simplify \(\frac{16^4}{4^6}\)?
3. What is \(9^{\frac{3}{2}}\) in simplified form?
4. How do you calculate \(\frac{125^2}{25^4}\)?
5. How do you simplify expressions with negative exponents?

**Tip:** When simplifying expressions with exponents, always look for a common base to make the process easier!

Learn how to simplify and solve the expression (27^3) / (9^5) step-by-step. This problem involves exponents and fractional exponents, demonstrating exponent rules and fractional exponent simplification. Suitable for high school students.

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