What will come in place of question mark (?) .
`A^(2//3) xx A^(3//2) xx A^(1//2) = ?`

Options

A. `A^(8//3)`
B. `A^(3//8)`
C. `A^(1//8)`
D. `A^(2//5)`

Answer

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

### Step 1: Write the expression
We start with the expression:
\[ A^{2/3} \times A^{3/2} \times A^{1/2} \]

### Step 2: Use the property of exponents
Since the bases are the same (all are \( A \)), we can add the exponents together:
\[ A^{(2/3) + (3/2) + (1/2)} \]

### Step 3: Find a common denominator
To add the fractions, we need to find a common denominator. The denominators are 3, 2, and 2. The least common multiple (LCM) of these numbers is 6.

### Step 4: Convert each fraction to have the common denominator
Now we convert each fraction:
- \( \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \)
- \( \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \)
- \( \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \)

### Step 5: Add the fractions
Now we can add the fractions:
\[ \frac{4}{6} + \frac{9}{6} + \frac{3}{6} = \frac{4 + 9 + 3}{6} = \frac{16}{6} \]

### Step 6: Simplify the fraction
Next, we simplify \( \frac{16}{6} \):
\[ \frac{16}{6} = \frac{8}{3} \]

### Step 7: Write the final expression
Thus, we have:
\[ A^{(8/3)} \]

### Final Answer
The final answer is:
\[ A^{8/3} \]

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