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The given expression is \( 125^{\frac{1}{3}} \). 

This represents the cube root of 125. To simplify this:

\[
125^{\frac{1}{3}} = \sqrt[3]{125}
\]

We know that:

\[
125 = 5 \times 5 \times 5 = 5^3
\]

Thus, the cube root of 125 is:

\[
\sqrt[3]{125} = 5
\]

So, \( 125^{\frac{1}{3}} = 5 \).

If you'd like more details or have further questions, let me know!

Here are some related questions to expand your understanding:

1. What is the cube root of 64?
2. How do you simplify \( 27^{\frac{2}{3}} \)?
3. What is the general method to evaluate \( x^{\frac{1}{n}} \)?
4. Can you find \( 343^{\frac{1}{3}} \)?
5. How does \( a^{\frac{m}{n}} \) work for non-integer values of \( m \) and \( n \)?

**Tip**: When simplifying exponents with fractions, remember that the denominator represents the root, and the numerator represents the power.

Simplify 125^{1/3} by calculating the cube root of 125. Learn how to apply the concept of fractional exponents and roots. Suitable for middle school students, grades 6-8.

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