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Let's evaluate the expressions one by one:

15. \( \sqrt{25} \)
\[ \sqrt{25} = 5 \]

16. \( \sqrt[4]{81} \)
\[ 81 = 3^4 \]
\[ \sqrt[4]{81} = 3 \]

17. \( \sqrt[3]{-128} \)
\[ -128 = (-2)^7 \]
\[ \sqrt[3]{-128} = -4 \]

18. \( \sqrt[3]{0.027} \)
\[ 0.027 = \left(\frac{3}{100}\right)^3 = \left(\frac{1}{10}\right)^3 \]
\[ \sqrt[3]{0.027} = 0.3 \]

19. \( \sqrt[4]{\frac{1}{16}} \)
\[ 16 = 2^4 \]
\[ \frac{1}{16} = \left(\frac{1}{2}\right)^4 \]
\[ \sqrt[4]{\frac{1}{16}} = \frac{1}{2} \]

20. \( \sqrt[3]{\frac{8}{27}} \)
\[ 8 = 2^3 \]
\[ 27 = 3^3 \]
\[ \frac{8}{27} = \left(\frac{2}{3}\right)^3 \]
\[ \sqrt[3]{\frac{8}{27}} = \frac{2}{3} \]

21. \( (49)^{1/2} \)
\[ 49 = 7^2 \]
\[ (49)^{1/2} = 7 \]

22. \( (64)^{1/3} \)
\[ 64 = 4^3 \]
\[ (64)^{1/3} = 4 \]

23. \( 27^{2/3} \)
\[ 27 = 3^3 \]
\[ 27^{2/3} = (3^3)^{2/3} = 3^2 = 9 \]

24. \( (9)^{-5/2} \)
\[ 9 = 3^2 \]
\[ (9)^{-5/2} = (3^2)^{-5/2} = 3^{-5} = \frac{1}{3^5} = \frac{1}{243} \]

25. \( (32)^{-2/5} \)
\[ 32 = 2^5 \]
\[ (32)^{-2/5} = (2^5)^{-2/5} = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \]

26. \( (0.09)^{-1/2} \)
\[ 0.09 = \left(\frac{3}{10}\right)^2 = \left(\frac{1}{10}\right)^2 \]
\[ (0.09)^{-1/2} = (0.3)^{-1} = \frac{1}{0.3} = 10/3 \approx 3.333 \]

27. \( \left( \frac{1}{32} \right)^{4/5} \)
\[ 32 = 2^5 \]
\[ \frac{1}{32} = (2^5)^{-1} = 2^{-5} \]
\[ \left( 2^{-5} \right)^{4/5} = 2^{-4} = \frac{1}{2^4} = \frac{1}{16} \]

28. \( \left( \frac{-27}{64} \right)^{4/3} \)
\[ -27 = (-3)^3 \]
\[ 64 = 4^3 \]
\[ \left( \frac{-27}{64} \right)^{4/3} = \left( \frac{(-3)^3}{4^3} \right)^{4/3} = \left( \frac{-3}{4} \right)^4 = \frac{81}{256} \]

Would you like more details or have any questions about these solutions? Here are some additional questions you might find interesting:

1. How do you simplify expressions with fractional exponents?
2. What is the process for evaluating negative bases with fractional exponents?
3. How can you rewrite radical expressions using exponents?
4. What are the rules for operations with radicals?
5. Can you explain the properties of exponents?

**Tip:** When working with fractional exponents, remember that \(a^{m/n} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m\). This property can help simplify many complex expressions.

Learn how to evaluate exponential and radical expressions step-by-step with detailed solutions. This problem covers key concepts such as exponents, roots, and radical notation. Suitable for high school students.

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