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To express \(\sqrt[3]{5}\) in the form of \(5^P\) where \(P\) is an integer, we can follow these steps:

The cube root of a number can be expressed as a fractional exponent. Specifically, \(\sqrt[3]{5}\) is equivalent to \(5\) raised to the power of \(\frac{1}{3}\). 

Therefore, we have:

\[
\sqrt[3]{5} = 5^{\frac{1}{3}}
\]

In this expression, \(P = \frac{1}{3}\), which is not an integer. However, it follows the required format of \(5^P\).

Would you like more details or have any questions about this solution?

Here are some related questions you might find interesting:

1. How do you express \(\sqrt[4]{7}\) in the form of \(7^P\)?
2. What is the general rule for converting \(n\)-th roots into fractional exponents?
3. How do you solve equations involving fractional exponents?
4. What are the properties of exponents and how are they applied?
5. How can you simplify expressions with exponents?
6. What is the relationship between exponents and logarithms?
7. How do you solve exponential equations?
8. What are some common applications of exponents in real-world problems?

**Tip:** Understanding the properties of exponents and roots is essential for simplifying complex algebraic expressions and solving equations. Always remember that roots can be expressed as fractional exponents, which can simplify many operations.

Learn how to express the cube root of 5 as 5 raised to the power of one-third (5^1/3). Understand the concept of fractional exponents and their application in mathematics. Suitable for advanced high school students.

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