https://file.aiquickdraw.com/mathbot/file/1725459983177u5sowsvs.jpg

The problem set requires writing expressions in radical and exponential forms. Here's how to convert each expression:

**I. Write each in radical form:**

1. \(\mathbf{8^{\frac{2}{3}}}\)  
   **Radical Form:** \(\sqrt[3]{8^2} = \sqrt[3]{64}\)

2. \(\mathbf{18^{\frac{1}{4}}}\)  
   **Radical Form:** \(\sqrt[4]{18}\)

3. \(\mathbf{(c^4d^3)^{\frac{1}{2}}}\)  
   **Radical Form:** \(\sqrt{c^4d^3}\)

4. \(\mathbf{(x^5y^6)^{\frac{1}{6}}}\)  
   **Radical Form:** \(\sqrt[6]{x^5y^6}\)

**II. Write each in exponential form:** 

If there are specific expressions for section II, please share them or clarify, and I will provide their exponential forms.

Would you like more details or have any questions?

**Here are 5 related questions to expand your understanding:**

1. How do you simplify expressions in radical form when possible?
2. What is the process for converting higher-order roots, such as the 5th root, into exponential form?
3. How can you rationalize the denominator in a fraction with a radical?
4. How do you handle expressions with variables when converting between radical and exponential forms?
5. What are the properties of exponents that are helpful in simplifying these expressions?

**Tip:** When dealing with fractional exponents, remember that the numerator represents the power, and the denominator represents the root. For example, \(a^{\frac{m}{n}} = \sqrt[n]{a^m}\).

Write each expression in radical form and exponential form as given in the image.

Learn how to convert algebraic expressions between radical and exponential forms. This problem set includes examples such as 8^(2/3) and (c^4d^3)^(1/2). Suitable for students in Grades 8-10.

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