https://file.aiquickdraw.com/mathbot/file/1725608640523jhf6l0zk.jpg

Let's go through the problems from the image one by one, transforming the radical expressions into exponential form.

### Problem 11: \(\sqrt[3]{8^7}\)
- **Radical form**: \(\sqrt[3]{8^7}\)
- **Exponential form**: \(8^{7/3}\)

### Problem 12: \(5 \sqrt[7]{y}\)
- **Radical form**: \(5 \sqrt[7]{y}\)
- **Exponential form**: \(5y^{1/7}\)

### Problem 13: \(-5 (2.3xyz)^{3}\)
- **Radical form**: \(-5 (2.3xyz)^{3}\)
- **Exponential form**: No transformation needed here, since this is already in exponential form.

### Problem 14: \(\sqrt[5]{(3xyz)^8}\)
- **Radical form**: \(\sqrt[5]{(3xyz)^8}\)
- **Exponential form**: \((3xyz)^{8/5}\)

### Problem 15: \(\sqrt[6]{(c^3)^2}\)
- **Radical form**: \(\sqrt[6]{(c^3)^2}\)
- **Exponential form**: \(c^{6/6} = c^1\)

Would you like further details on any of the transformations?

Here are 5 relative questions to consider:
1. How do fractional exponents relate to radicals in general?
2. Can any radical expression be expressed as a fractional exponent?
3. What happens if the exponent in the exponential form is a negative fraction?
4. How would you simplify expressions with multiple bases and exponents?
5. How do you handle radicals and exponents when variables are involved?

**Tip**: Always remember that \( \sqrt[n]{x^m} \) translates to \( x^{m/n} \) in exponential form!

Transform the given radical form into exponential form and exponential form.

Learn how to transform radical expressions into exponential form with step-by-step solutions. This guide covers core concepts of exponents and radicals, with detailed examples suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation