1/2 multiplied by ((u)^(3/2))/(3/2) whats the answer? how can i work with fractions like this?

To solve the expression \( \frac{1}{2} \times \frac{u^{3/2}}{3/2} \), follow these steps:

### Step-by-Step Solution:

1. **Simplify the product of fractions**:
   Recall that multiplying fractions is straightforward: multiply the numerators and multiply the denominators. 

   \[
   \frac{1}{2} \times \frac{u^{3/2}}{3/2} = \frac{1 \cdot u^{3/2}}{2 \cdot \frac{3}{2}}
   \]

2. **Simplify the denominator**:
   When you have \( 2 \times \frac{3}{2} \), simplify it:
   
   \[
   2 \times \frac{3}{2} = \frac{6}{2} = 3
   \]

   So now the expression becomes:
   \[
   \frac{u^{3/2}}{3}
   \]

Thus, the final simplified expression is:

\[
\frac{u^{3/2}}{3}
\]

### Working with Fractions in General

When working with fractions:
1. **Multiplying fractions**: Multiply the numerators together and the denominators together.
   \[
   \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
   \]

2. **Dividing fractions**: Flip (take the reciprocal of) the second fraction and multiply.
   \[
   \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
   \]

3. **Simplifying complex expressions**: Always simplify each term before multiplying or dividing to avoid errors. Reduce common factors in both the numerator and denominator when possible.

Would you like more details on how to handle fractional powers or any other specifics?

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### 5 Related Questions:
1. How do you multiply and divide fractions with exponents?
2. What does \( u^{3/2} \) mean in terms of roots and powers?
3. How do you simplify complex fractions step by step?
4. Can you explain how to add or subtract fractions with different denominators?
5. How can we apply fractional exponents in calculus?

### Tip:
Always look for common factors between the numerator and denominator to simplify fractions early in the process.

Solve the expression (1/2) multiplied by (u^(3/2))/(3/2) with a detailed step-by-step explanation. Learn key algebraic concepts like multiplying fractions and handling fractional exponents. Ideal for students in Grades 9-11.

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