To solve \( 25^{\frac{3}{2}} \), we break it down as follows:

1. The fractional exponent \( \frac{3}{2} \) can be interpreted as:
   \[
   25^{\frac{3}{2}} = \left( 25^{\frac{1}{2}} \right)^3
   \]
2. \( 25^{\frac{1}{2}} \) means the square root of 25, which is 5:
   \[
   25^{\frac{1}{2}} = 5
   \]
3. Now, cube the result:
   \[
   5^3 = 125
   \]

Thus, \( 25^{\frac{3}{2}} = 125 \).

Would you like a further breakdown of these steps or have any questions?

Here are some related questions to explore:

1. What is \( 16^{\frac{3}{2}} \)?
2. How do you calculate \( 9^{\frac{5}{2}} \)?
3. What is the general method to solve any expression with fractional exponents?
4. How does \( 25^{\frac{2}{3}} \) compare to \( 25^{\frac{3}{2}} \)?
5. Can fractional exponents be negative, and what would that look like for \( 25^{-\frac{3}{2}} \)?

**Tip:** Fractional exponents can be split into two steps: a root (denominator) and a power (numerator).

Explore how to solve 25 raised to the power of 3/2, a problem involving fractional exponents. Learn the step-by-step process, which includes calculating square roots and powers. Ideal for students in Grades 8-10.

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