The expression \((a^{1/2})^{3/2}\) can be simplified using the laws of exponents.

### Step-by-step process:
1. Apply the power of a power rule, which states \((a^m)^n = a^{m \cdot n}\).
   \[
   (a^{1/2})^{3/2} = a^{(1/2) \cdot (3/2)} = a^{3/4}
   \]

So, the simplified expression is:
\[
a^{3/4}
\]

Would you like more details or have any questions?

Here are some related problems for practice:
1. Simplify \((b^{1/3})^{5/4}\).
2. Simplify \((c^{2/3})^{3/2}\).
3. Express \((x^{4/5})^{5/6}\) in its simplest form.
4. What is \((y^{3/2})^{2/3}\)?
5. Simplify \((z^{5/4})^{4/5}\).

**Tip:** Always apply the power rule \((a^m)^n = a^{m \cdot n}\) when simplifying nested exponent expressions.

This webpage provides a detailed explanation of how to simplify the exponential expression (a^1/2)^3/2 using the laws of exponents. Learn how to apply the power of a power rule to simplify nested exponent expressions. Suitable for students in Grades 8-10.

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