https://file.aiquickdraw.com/mathbot/file/1726302626903f9yhkqm4.jpg

To solve \( 2^{3/2} \), follow these steps:

1. **Interpretation of the exponent**: The expression \( 2^{3/2} \) can be written as:
   \[
   2^{3/2} = \left(2^3\right)^{1/2}
   \]
   which means the square root of \( 2^3 \).

2. **Evaluate \( 2^3 \)**: 
   \[
   2^3 = 8
   \]
   So now the expression becomes:
   \[
   \sqrt{8}
   \]

3. **Simplify \( \sqrt{8} \)**: 
   The square root of 8 can be simplified as:
   \[
   \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
   \]

Thus, \( 2^{3/2} = 2\sqrt{2} \).

If you have any questions or need further details, feel free to ask!

### Related questions:
1. How can you simplify fractional exponents like \( a^{m/n} \)?
2. What are the properties of exponents when simplifying radical expressions?
3. How would you solve \( 3^{5/3} \) similarly?
4. What is the relationship between radicals and fractional exponents?
5. How does the power rule apply in integration when exponents are involved?

### Tip:
When simplifying expressions with fractional exponents, remember that \( a^{m/n} \) is the same as \( \sqrt[n]{a^m} \), which can often simplify more easily by breaking it into steps.

Learn how to solve 2^(3/2) step by step using the laws of exponents. This solution covers interpreting fractional exponents, simplifying radicals, and applying exponent rules, ideal for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation