Let's simplify the expression \(\left(\frac{u^3}{10}\right)^2\).

### Step 1: Apply the exponent to both the numerator and the denominator.
The expression can be expanded as:

\[
\left(\frac{u^3}{10}\right)^2 = \frac{(u^3)^2}{10^2}
\]

### Step 2: Simplify the numerator and denominator.
Now, simplify both parts:

- The numerator: \((u^3)^2 = u^{3 \times 2} = u^6\)
- The denominator: \(10^2 = 100\)

So the expression simplifies to:

\[
\frac{u^6}{100}
\]

### Final Answer:
The simplified expression is \(\frac{u^6}{100}\).

Would you like to explore further details or have any other questions?

Here are some related questions you might find interesting:

1. How do you simplify expressions with fractional exponents?
2. What is the power of a power rule in exponents?
3. How do you multiply expressions with the same base but different exponents?
4. How do you divide expressions with the same base but different exponents?
5. How do you handle exponents when they are negative?

**Tip:** When dealing with exponents, remember that the power of a product can be distributed to both the numerator and the denominator.

Learn how to simplify the expression (u^3 / 10)^2 with a detailed step-by-step solution. This problem involves exponents and fractional exponents, showing how to apply exponent rules effectively. Suitable for high school students and those preparing for advanced mathematics.

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