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The question in the image asks to simplify the given expression \( 2^{3/2} \) in terms of fractional exponents.

### Step-by-step simplification:

1. The given expression is \( 2^{3/2} \).
2. We know that a fractional exponent \( a^{m/n} \) represents the \( n \)-th root of \( a^m \). So:
   \[
   2^{3/2} = \left( 2^3 \right)^{1/2} = \sqrt{2^3}
   \]
3. Simplifying \( 2^3 \):
   \[
   2^3 = 8
   \]
   So:
   \[
   2^{3/2} = \sqrt{8}
   \]
4. Now, simplify \( \sqrt{8} \):
   \[
   \sqrt{8} = \sqrt{4 \cdot 2} = 2 \sqrt{2}
   \]
   
Thus, \( 2^{3/2} \) simplifies to \( 2 \sqrt{2} \).

In terms of the answer choices, none of the options directly show \( 2 \sqrt{2} \). However, based on the question, if the answers are left in exponent form, the correct option would likely be the one that still matches \( 2^{3/2} \), which should be represented as \( 2^{3/2} \).

### Do you have any further questions or need clarification? Here are five related questions:
1. How do you convert fractional exponents to radicals and back?
2. How can you simplify other powers like \( a^{5/3} \)?
3. What is the relationship between roots and exponents?
4. How would you graph an exponential function with a fractional exponent?
5. How does the concept of fractional exponents extend to negative bases?

**Tip:** Always check if the given expression can be simplified before applying any exponent rules.

Simplify the following expression in terms of fractional exponents: 2^(3/2)

This guide provides a detailed solution to simplifying the expression 2^(3/2). It explains the conversion between fractional exponents and radicals, offering a step-by-step process to arrive at the final simplified form 2√2. Suitable for high school students.

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